Representations of finite groups of Lie type

Curtis, Charles W.

doi:10.1090/S0273-0979-1979-14648-2

Representations of finite groups of Lie type
HTML articles powered by AMS MathViewer

by Charles W. Curtis PDF

Bull. Amer. Math. Soc. 1 (1979), 721-757

References

Ferdinand Georg Frobenius, Gesammelte Abhandlungen. Bände I, II, III, Springer-Verlag, Berlin-New York, 1968 (German). Herausgegeben von J.-P. Serre. MR 0235974
Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Die Grundlehren der mathematischen Wissenschaften, Band 188, Springer-Verlag, New York-Heidelberg, 1972. MR 0498999
C. T. Benson, On the generic algebra of a unipotent, Comm. Algebra 5 (1977), no. 8, 841–862. MR 447421, DOI 10.1080/00927877708822198
Clark T. Benson, The generic degrees of the irreducible characters of $E_{8}$, Comm. Algebra 7 (1979), no. 11, 1199–1209. MR 535928, DOI 10.1080/00927877908822397
C. T. Benson and C. W. Curtis, On the degrees and rationality of certain characters of finite Chevalley groups, Trans. Amer. Math. Soc. 165 (1972), 251–273. MR 304473, DOI 10.1090/S0002-9947-1972-0304473-1
Clark T. Benson, Larry C. Grove, and David B. Surowski, Semilinear automorphisms and dimension functions for certain characters of finite Chevalley groups, Math. Z. 144 (1975), no. 2, 149–159. MR 382468, DOI 10.1007/BF01190944
Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
Armand Borel, Properties and linear representations of Chevalley groups, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 1–55. MR 0258838
Armand Borel and Jacques Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150 (French). MR 207712, DOI 10.1007/BF02684375
A. Borel and J. Tits, Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I, Invent. Math. 12 (1971), 95–104 (French). MR 294349, DOI 10.1007/BF01404653
N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
R. W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1–59. MR 318337
Roger W. Carter, Simple groups of Lie type, Pure and Applied Mathematics, Vol. 28, John Wiley & Sons, London-New York-Sydney, 1972. MR 0407163
R. W. Carter, Centralizers of semisimple elements in finite groups of Lie type, Proc. London Math. Soc. (3) 37 (1978), no. 3, 491–507. MR 512022, DOI 10.1112/plms/s3-37.3.491
Bomshik Chang and Rimhak Ree, The characters of $G_{2}(q)$, Symposia Mathematica, Vol. XIII (Convegno di Gruppi e loro Rappresentazioni, INDAM, Rome,1972), Academic Press, London, 1974, pp. 395–413. MR 0364419
C. Chevalley, Sur certains groupes simples, Tohoku Math. J. (2) 7 (1955), 14–66 (French). MR 73602, DOI 10.2748/tmj/1178245104
Charles W. Curtis, The Steinberg character of a finite group with a $(B,\,N)$-pair, J. Algebra 4 (1966), 433–441. MR 201524, DOI 10.1016/0021-8693(66)90033-0
Charles W. Curtis, On the values of certain irreducible characters of finite Chevalley groups, Symposia Mathematica, Vol. XIII (Convegno di Gruppi e loro Rappresentazioni, INDAM, Rome, 1972) Academic Press, London, 1974, pp. 343–355. MR 0369561
Charles W. Curtis, Reduction theorems for characters of finite groups of Lie type, J. Math. Soc. Japan 27 (1975), no. 4, 666–688. MR 399282, DOI 10.2969/jmsj/02740666
Charles W. Curtis, A note on the connections between the generalized characters of Deligne and Lusztig and the cuspidal characters of reductive groups over finite fields, J. London Math. Soc. (2) 14 (1976), no. 3, 405–412. MR 435238, DOI 10.1112/jlms/s2-14.3.405
Charles W. Curtis and Timothy V. Fossum, On centralizer rings and characters of representations of finite groups, Math. Z. 107 (1968), 402–406. MR 237665, DOI 10.1007/BF01110070
C. W. Curtis, N. Iwahori, and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with $(B,$ $N)$-pairs, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 81–116. MR 347996, DOI 10.1007/BF02684695
Charles W. Curtis, William M. Kantor, and Gary M. Seitz, The $2$-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1–59. MR 422440, DOI 10.1090/S0002-9947-1976-0422440-8
P. Deligne, Cohomologie étale, Lecture Notes in Mathematics, vol. 569, Springer-Verlag, Berlin, 1977 (French). Séminaire de géométrie algébrique du Bois-Marie SGA $4\frac {1}{2}$. MR 463174, DOI 10.1007/BFb0091526
P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103–161. MR 393266, DOI 10.2307/1971021
Leonard Eugene Dickson, Linear groups: With an exposition of the Galois field theory, Dover Publications, Inc., New York, 1958. With an introduction by W. Magnus. MR 0104735
Jean Dieudonné, La géométrie des groupes classiques, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 5, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (French). MR 0072144
Hikoe Enomoto, The characters of the finite Chevalley group $G_{2}(q),q=3^{f}$, Japan. J. Math. (N.S.) 2 (1976), no. 2, 191–248. MR 437628, DOI 10.4099/math1924.2.191
Paul Fong and Gary M. Seitz, Groups with a $(B,\,N)$-pair of rank $2$. I, II, Invent. Math. 21 (1973), 1–57; ibid. 24 (1974), 191–239. MR 354858, DOI 10.1007/BF01389689
J. S. Frame, The classes and representations of the groups of $27$ lines and $28$ bitangents, Ann. Mat. Pura Appl. (4) 32 (1951), 83–119. MR 47038, DOI 10.1007/BF02417955
J. S. Frame, The characters of the Weyl group $E_{8}$, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 111–130. MR 0269751
Howard Garland, $p$-adic curvature and the cohomology of discrete subgroups of $p$-adic groups, Ann. of Math. (2) 97 (1973), 375–423. MR 320180, DOI 10.2307/1970829
S. I. Gel′fand, Representations of the full linear group over a finite field, Mat. Sb. (N.S.) 83 (125) (1970), 15–41. MR 0272916
J. A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc. 80 (1955), 402–447. MR 72878, DOI 10.1090/S0002-9947-1955-0072878-2
James A. Green, On the Steinberg characters of finite Chevalley groups, Math. Z. 117 (1970), 272–288. MR 280612, DOI 10.1007/BF01109848
A. Grothendieck, Groupes diagonalisables, Schémas en Groupes (Sém. Géométrie Algébrique, Inst. Hautes Études Sci., 1963/64) Inst. Hautes Études Sci., Paris, 1964, pp. Fasc. 3, Exposé 8, 36 (French). MR 0212024
Harish-Chandra, Eisenstein series over finite fields, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 76–88. MR 0457579
Robert B. Howlett, On the degrees of Steinberg characters of Chevalley groups, Math. Z. 135 (1973/74), 125–135. MR 360781, DOI 10.1007/BF01189349
Nagayoshi Iwahori, On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. I 10 (1964), 215–236 (1964). MR 165016
Noriaki Kawanaka, A theorem on finite Chevalley groups, Osaka Math. J. 10 (1973), 1–13. MR 332948
Noriaki Kawanaka, Unipotent elements and characters of finite Chevalley groups, Osaka Math. J. 12 (1975), no. 2, 523–554. MR 384914
D. Kazhdan, On $\varepsilon$-representations, Israel J. Math. 43 (1982), no. 4, 315–323. MR 693352, DOI 10.1007/BF02761236
Robert W. Kilmoyer, Principal series representations of finite Chevalley groups, J. Algebra 51 (1978), no. 1, 300–319. MR 487479, DOI 10.1016/0021-8693(78)90149-7
Takeshi Kondo, The characters of the Weyl group of type $F_{4}$, J. Fac. Sci. Univ. Tokyo Sect. I 11 (1965), 145–153 (1965). MR 185018
Bertram Kostant, Groups over $Z$, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 90–98. MR 0207713
G. I. Lehrer, Adjoint groups, regular unipotent elements and discrete series characters, Trans. Amer. Math. Soc. 214 (1975), 249–260. MR 384915, DOI 10.1090/S0002-9947-1975-0384915-9
George Lusztig, The discrete series of $GL_{n}$ over a finite field, Annals of Mathematics Studies, No. 81, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0382419
G. Lusztig, On the Green polynomials of classical groups, Proc. London Math. Soc. (3) 33 (1976), no. 3, 443–475. MR 424959, DOI 10.1112/plms/s3-33.3.443
G. Lusztig, Coxeter orbits and eigenspaces of Frobenius, Invent. Math. 38 (1976/77), no. 2, 101–159. MR 453885, DOI 10.1007/BF01408569
G. Lusztig, On the finiteness of the number of unipotent classes, Invent. Math. 34 (1976), no. 3, 201–213. MR 419635, DOI 10.1007/BF01403067
G. Lusztig, Irreducible representations of finite classical groups, Invent. Math. 43 (1977), no. 2, 125–175. MR 463275, DOI 10.1007/BF01390002
George Lusztig, Representations of finite Chevalley groups, CBMS Regional Conference Series in Mathematics, vol. 39, American Mathematical Society, Providence, R.I., 1978. Expository lectures from the CBMS Regional Conference held at Madison, Wis., August 8–12, 1977. MR 518617, DOI 10.1090/cbms/039
George Lusztig and Bhama Srinivasan, The characters of the finite unitary groups, J. Algebra 49 (1977), no. 1, 167–171. MR 453886, DOI 10.1016/0021-8693(77)90277-0
Hideya Matsumoto, Générateurs et relations des groupes de Weyl généralisés, C. R. Acad. Sci. Paris 258 (1964), 3419–3422 (French). MR 183818
Forrest Richen, Modular representations of split $BN$ pairs, Trans. Amer. Math. Soc. 140 (1969), 435–460. MR 242972, DOI 10.1090/S0002-9947-1969-0242972-1
Gary M. Seitz, Flag-transitive subgroups of Chevalley groups, Ann. of Math. (2) 97 (1973), 27–56. MR 340446, DOI 10.2307/1970876
Louis Solomon, The Steinberg character of a finite group with $BN$-pair, Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969, pp. 213–221. MR 0246951
Louis Solomon, On the affine group over a finite field, Representation theory of finite groups and related topics (Proc. Sympos. Pure Math., Vol. XXI, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 145–147. MR 0318287
Louis Solomon, The affine group. I. Bruhat decomposition, J. Algebra 20 (1972), 512–539. MR 306349, DOI 10.1016/0021-8693(72)90071-3
T. A. Springer, Cusp forms for finite groups, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 97–120. MR 0263942
T. A. Springer, Generalization of Green’s polynomials, Representation theory of finite groups and related topics (Proc. Sympos. Pure Math., Vol. XXI, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 149–153. MR 0327926
T. A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173–207. MR 442103, DOI 10.1007/BF01390009
T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 167–266. MR 0268192
Bhama Srinivasan, The characters of the finite symplectic group $\textrm {Sp}(4,\,q)$, Trans. Amer. Math. Soc. 131 (1968), 488–525. MR 220845, DOI 10.1090/S0002-9947-1968-0220845-7
Bhama Srinivasan, On the Steinberg character of a finite simple group of Lie type, J. Austral. Math. Soc. 12 (1971), 1–14. MR 0291317, DOI 10.1017/S1446788700008247
Bhama Srinivasan, Green polynomials of finite classical groups, Comm. Algebra 5 (1977), no. 12, 1241–1258. MR 498889, DOI 10.1080/00927877708822217
R. Steinberg, A geometric approach to the representations of the full linear group over a Galois field, Trans. Amer. Math. Soc. 71 (1951), 274–282. MR 43784, DOI 10.1090/S0002-9947-1951-0043784-0
Robert Steinberg, Prime power representations of finite linear groups. II, Canadian J. Math. 9 (1957), 347–351. MR 87659, DOI 10.4153/CJM-1957-041-1
Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728
David B. Surowski, Representations of a subalgebra of the generic algebra corresponding to the Weyl group of type $F_{4}$, Comm. Algebra 5 (1977), no. 8, 873–888. MR 442104, DOI 10.1080/00927877708822200
David B. Surowski, Degrees of irreducible characters of $(B,\,N)$-pairs of types $E_{6}$ and $E_{7}$, Trans. Amer. Math. Soc. 243 (1978), 235–249. MR 502905, DOI 10.1090/S0002-9947-1978-0502905-2
Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099
André Weil, Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497–508. MR 29393, DOI 10.1090/S0002-9904-1949-09219-4

AMS Website Down

Bulletin of the American Mathematical Society

Representations of finite groups of Lie type
HTML articles powered by AMS MathViewer