Bulletin of the American Mathematical Society

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Book Information:

Author: James Arthur
Title: The endoscopic classification of representations—orthogonal and symplectic groups
Additional book information: AMS Colloquium Publications, Vol. 61, American Mathematical Society, Providence, Rhode Island, 2013, xviii+590 pp., ISBN 978-0-8218-4990-3, $115.00

Jeffrey Adams, Dan Barbasch, and David A. Vogan Jr., The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992. MR 1162533, DOI 10.1007/978-1-4612-0383-4

James Arthur, An introduction to the trace formula, Harmonic analysis, the trace formula, and Shimura varieties, Clay Math. Proc., vol. 4, Amer. Math. Soc., Providence, RI, 2005, pp. 1–263. MR 2192011

James Arthur, A trace formula for reductive groups I: Terms associated to classes in $G(\mathbb {Q})$, Duke Math. J. 245 1978, 911–952

James Arthur, A trace formula for reductive groups. II. Applications of a truncation operator, Compositio Math. 40 (1980), no. 1, 87–121. MR 558260

James Arthur, Unipotent automorphic representations: conjectures, Astérisque 171-172 1989, 13–71

James Arthur, A stable trace formula. II. Global descent, Invent. Math. 143 (2001), no. 1, 157–220. MR 1802795, DOI 10.1007/s002220000107

James Arthur, A stable trace formula. I. General expansions, J. Inst. Math. Jussieu 1 (2002), no. 2, 175–277. MR 1954821, DOI 10.1017/S1474-748002000051

James Arthus, A stable trace formula. III. Proof of the main theorems, Annals of Math. 158 2003, 769–873

James Arthur, Intertwining operators and residues. I. Weighted characters, J. Funct. Anal. 84 (1989), no. 1, 19–84. MR 999488, DOI 10.1016/0022-1236(89)90110-9

James Arthur, On a family of distributions obtained from Eisenstein series. II. Explicit formulas, Amer. J. Math. 104 (1982), no. 6, 1289–1336. MR 681738, DOI 10.2307/2374062

James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, Princeton, NJ, 1989. MR 1007299

A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61. MR 546608

A. Borel and H. Jacquet, Automorphic forms and automorphic representations, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 189–207. With a supplement “On the notion of an automorphic representation” by R. P. Langlands. MR 546598

J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to $\textrm {GL}_N$, Publ. Math. Inst. Hautes Études Sci. 93 (2001), 5–30. MR 1863734, DOI 10.1007/s10240-001-8187-z

J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci., 99 2004, 163-233

Stephen S. Gelbart, Automorphic forms on adèle groups, Annals of Mathematics Studies, No. 83, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0379375

Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of $\textrm {GL}(2)$ and $\textrm {GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066

David Ginzburg, Stephen Rallis, and David Soudry, The descent map from automorphic representations of $\textrm {GL}(n)$ to classical groups, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. MR 2848523, DOI 10.1142/9789814304993

Thomas C. Hales, The subregular germ of orbital integrals, Mem. Amer. Math. Soc. 99 (1992), no. 476, xii+142. MR 1124110, DOI 10.1090/memo/0476

Michael Harris and Richard Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001. With an appendix by Vladimir G. Berkovich. MR 1876802

Guy Henniart, Une preuve simple des conjectures de Langlands pour $\textrm {GL}(n)$ sur un corps $p$-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446, DOI 10.1007/s002220050012

H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), no. 2, 367–464. MR 701565, DOI 10.2307/2374264

H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic forms. II, Amer. J. Math. 103 (1981), no. 4, 777–815. MR 623137, DOI 10.2307/2374050

C. David Keys and Freydoon Shahidi, Artin $L$-functions and normalization of intertwining operators, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 1, 67–89. MR 944102

Henry H. Kim, Functoriality for the exterior square of $\textrm {GL}_4$ and the symmetric fourth of $\textrm {GL}_2$, J. Amer. Math. Soc. 16 (2003), no. 1, 139–183. With appendix 1 by Dinakar Ramakrishnan and appendix 2 by Kim and Peter Sarnak. MR 1937203, DOI 10.1090/S0894-0347-02-00410-1

Henry H. Kim and Freydoon Shahidi, Functorial products for $\textrm {GL}_2\times \textrm {GL}_3$ and the symmetric cube for $\textrm {GL}_2$, Ann. of Math. (2) 155 (2002), no. 3, 837–893. With an appendix by Colin J. Bushnell and Guy Henniart. MR 1923967, DOI 10.2307/3062134

Robert E. Kottwitz and Diana Shelstad, Foundations of twisted endoscopy, Astérisque 255 (1999), vi+190 (English, with English and French summaries). MR 1687096

J.-P. Labesse and R. P. Langlands, $L$-indistinguishability for $\textrm {SL}(2)$, Canadian J. Math. 31 (1979), no. 4, 726–785. MR 540902, DOI 10.4153/CJM-1979-070-3

Jean-Pierre Labesse and Jean-Loup Waldspurger, La formule des traces tordue d’après le Friday Morning Seminar, CRM Monograph Series, vol. 31, American Mathematical Society, Providence, RI, 2013 (French). With a foreword by Robert Langlands [dual English/French text]. MR 3026269, DOI 10.1090/crmm/031

R. P. Langlands, Problems in the theory of automorphic forms, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 18–61. MR 0302614

R. P. Langlands, Euler products, Yale University Press, 1971

R. P. Langlands, Les débuts d’une formule des traces stables, Publ. Math. Univ. Paris VII 13, 1983

Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808

R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation theory and harmonic analysis on semisimple Lie groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170. MR 1011897, DOI 10.1090/surv/031/03

R. P. Langlands, Beyond endoscopy, in Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins University Press, 2004, 611–698

R. P. Langlands and D. Shelstad, On the definition of transfer factors, Math. Ann. 278 (1987), no. 1-4, 219–271. MR 909227, DOI 10.1007/BF01458070

R. P. Langlands and D. Shelstad, Descent for transfer factors, The Grothendieck Festschift, Vol. II, Birkhäuser, Boston, 1990, 485-563

C. Mœglin and J.-L. Waldspurger, Le spectre résiduel de $\textrm {GL}(n)$, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 4, 605–674 (French). MR 1026752

C. Mœglin and J.-L. Waldspurger, Stabilisation de la formule des traces tordue, Vol. 1, Progress in Mathematics, 316, 2016

C. Mœglin and J.-L. Waldspurger, Stabilisation de la formule des traces tordue, Vol. 2, Progress in Mathematics, 317, 2016

Bao Châu Ngô, Le lemme fondamental pour les algèbres de Lie, Publ. Math. Inst. Hautes Études Sci. 111 (2010), 1–169 (French). MR 2653248, DOI 10.1007/s10240-010-0026-7

Dinakar Ramakrishnan, Modularity of the Rankin-Selberg $L$-series, and multiplicity one for $\textrm {SL}(2)$, Ann. of Math. (2) 152 (2000), no. 1, 45–111. MR 1792292, DOI 10.2307/2661379

Peter Scholze, The local Langlands correspondence for $\mathrm {GL}_n$ over $p$-adic fields, Invent. Math. 192 (2013), no. 3, 663–715. MR 3049932, DOI 10.1007/s00222-012-0420-5

Freydoon Shahidi, A proof of Langlands’ conjecture on Plancherel measures; complementary series for $p$-adic groups, Ann. of Math. (2) 132 (1990), no. 2, 273–330. MR 1070599, DOI 10.2307/1971524

Freydoon Shahidi, Eisenstein series and automorphic $L$-functions, American Mathematical Society Colloquium Publications, vol. 58, American Mathematical Society, Providence, RI, 2010. MR 2683009, DOI 10.1090/coll/058

D. Shelstad, $L$-indistinguishability for real groups, Math. Ann. 259 (1982), no. 3, 385–430. MR 661206, DOI 10.1007/BF01456950

• Jeffrey Adams, Dan Barbasch, and David A. Vogan Jr., The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992. MR 1162533, DOI 10.1007/978-1-4612-0383-4
• James Arthur, An introduction to the trace formula, Harmonic analysis, the trace formula, and Shimura varieties, Clay Math. Proc., vol. 4, Amer. Math. Soc., Providence, RI, 2005, pp. 1–263. MR 2192011
• James Arthur, A trace formula for reductive groups I: Terms associated to classes in $G(\mathbb {Q})$, Duke Math. J. 245 1978, 911–952
• James Arthur, A trace formula for reductive groups. II. Applications of a truncation operator, Compositio Math. 40 (1980), no. 1, 87–121. MR 558260
• James Arthur, Unipotent automorphic representations: conjectures, Astérisque 171-172 1989, 13–71
• James Arthur, A stable trace formula. II. Global descent, Invent. Math. 143 (2001), no. 1, 157–220. MR 1802795, DOI 10.1007/s002220000107
• James Arthur, A stable trace formula. I. General expansions, J. Inst. Math. Jussieu 1 (2002), no. 2, 175–277. MR 1954821, DOI 10.1017/S1474-748002000051
• James Arthus, A stable trace formula. III. Proof of the main theorems, Annals of Math. 158 2003, 769–873
• James Arthur, Intertwining operators and residues. I. Weighted characters, J. Funct. Anal. 84 (1989), no. 1, 19–84. MR 999488, DOI 10.1016/0022-1236(89)90110-9
• James Arthur, On a family of distributions obtained from Eisenstein series. II. Explicit formulas, Amer. J. Math. 104 (1982), no. 6, 1289–1336. MR 681738, DOI 10.2307/2374062
• James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, Princeton, NJ, 1989. MR 1007299
• A. Borel, Automorphic $L$-functions, in Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61. MR 546608
• A. Borel and H. Jacquet, Automorphic forms and automorphic representations, in Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 189–207. With a supplement “On the notion of an automorphic representation” by R. P. Langlands. MR 546598
• J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to $\textrm {GL}_N$, Publ. Math. Inst. Hautes Études Sci. 93 (2001), 5–30. MR 1863734, DOI 10.1007/s10240-001-8187-z
• J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci., 99 2004, 163-233
• Stephen S. Gelbart, Automorphic forms on adèle groups, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. Annals of Mathematics Studies, No. 83. MR 0379375
• Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of $\textrm {GL}(2)$ and $\textrm {GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066
• David Ginzburg, Stephen Rallis, and David Soudry, The descent map from automorphic representations of $\textrm {GL}(n)$ to classical groups, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. MR 2848523, DOI 10.1142/9789814304993
• Thomas C. Hales, The subregular germ of orbital integrals, Mem. Amer. Math. Soc. 99 (1992), no. 476, xii+142. MR 1124110, DOI 10.1090/memo/0476
• Michael Harris and Richard Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001. With an appendix by Vladimir G. Berkovich. MR 1876802
• Guy Henniart, Une preuve simple des conjectures de Langlands pour $\textrm {GL}(n)$ sur un corps $p$-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446, DOI 10.1007/s002220050012
• H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), no. 2, 367–464. MR 701565, DOI 10.2307/2374264
• H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic forms. II, Amer. J. Math. 103 (1981), no. 4, 777–815. MR 623137, DOI 10.2307/2374050
• C. David Keys and Freydoon Shahidi, Artin $L$-functions and normalization of intertwining operators, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 1, 67–89. MR 944102
• Henry H. Kim, Functoriality for the exterior square of $\textrm {GL}_4$ and the symmetric fourth of $\textrm {GL}_2$, J. Amer. Math. Soc. 16 (2003), no. 1, 139–183. With appendix 1 by Dinakar Ramakrishnan and appendix 2 by Kim and Peter Sarnak. MR 1937203, DOI 10.1090/S0894-0347-02-00410-1
• Henry H. Kim and Freydoon Shahidi, Functorial products for $\textrm {GL}_2\times \textrm {GL}_3$ and the symmetric cube for $\textrm {GL}_2$, Ann. of Math. (2) 155 (2002), no. 3, 837–893. With an appendix by Colin J. Bushnell and Guy Henniart. MR 1923967, DOI 10.2307/3062134
• Robert E. Kottwitz and Diana Shelstad, Foundations of twisted endoscopy, Astérisque 255 (1999), vi+190 (English, with English and French summaries). MR 1687096
• J.-P. Labesse and R. P. Langlands, $L$-indistinguishability for $\textrm {SL}(2)$, Canad. J. Math. 31 (1979), no. 4, 726–785. MR 540902, DOI 10.4153/CJM-1979-070-3
• Jean-Pierre Labesse and Jean-Loup Waldspurger, La formule des traces tordue d’après le Friday Morning Seminar, CRM Monograph Series, vol. 31, American Mathematical Society, Providence, RI, 2013 (French). With a foreword by Robert Langlands [dual English/French text]. MR 3026269
• R. P. Langlands, Problems in the theory of automorphic forms, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 18–61. Lecture Notes in Math., Vol. 170. MR 0302614
• R. P. Langlands, Euler products, Yale University Press, 1971
• R. P. Langlands, Les débuts d’une formule des traces stables, Publ. Math. Univ. Paris VII 13, 1983
• Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, vol. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808
• R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation theory and harmonic analysis on semisimple Lie groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170. MR 1011897, DOI 10.1090/surv/031/03
• R. P. Langlands, Beyond endoscopy, in Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins University Press, 2004, 611–698
• R. P. Langlands and D. Shelstad, On the definition of transfer factors, Math. Ann. 278 (1987), no. 1-4, 219–271. MR 909227, DOI 10.1007/BF01458070
• R. P. Langlands and D. Shelstad, Descent for transfer factors, The Grothendieck Festschift, Vol. II, Birkhäuser, Boston, 1990, 485-563
• C. Mœglin and J.-L. Waldspurger, Le spectre résiduel de $\textrm {GL}(n)$, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 4, 605–674 (French). MR 1026752
• C. Mœglin and J.-L. Waldspurger, Stabilisation de la formule des traces tordue, Vol. 1, Progress in Mathematics, 316, 2016
• C. Mœglin and J.-L. Waldspurger, Stabilisation de la formule des traces tordue, Vol. 2, Progress in Mathematics, 317, 2016
• Bao Châu Ngô, Le lemme fondamental pour les algèbres de Lie, Publ. Math. Inst. Hautes Études Sci. 111 (2010), 1–169 (French). MR 2653248, DOI 10.1007/s10240-010-0026-7
• Dinakar Ramakrishnan, Modularity of the Rankin-Selberg $L$-series, and multiplicity one for $\textrm {SL}(2)$, Ann. of Math. (2) 152 (2000), no. 1, 45–111. MR 1792292, DOI 10.2307/2661379
• Peter Scholze, The local Langlands correspondence for $\mathrm {GL}_n$ over $p$-adic fields, Invent. Math. 192 (2013), no. 3, 663–715. MR 3049932, DOI 10.1007/s00222-012-0420-5
• Freydoon Shahidi, A proof of Langlands’ conjecture on Plancherel measures; complementary series for $p$-adic groups, Ann. of Math. (2) 132 (1990), no. 2, 273–330. MR 1070599, DOI 10.2307/1971524
• Freydoon Shahidi, Eisenstein series and automorphic $L$-functions, American Mathematical Society Colloquium Publications, vol. 58, American Mathematical Society, Providence, RI, 2010. MR 2683009, DOI 10.1090/coll/058
• D. Shelstad, $L$-indistinguishability for real groups, Math. Ann. 259 (1982), no. 3, 385–430. MR 661206, DOI 10.1007/BF01456950