Tempered non-discrete spectrum for pseudo-$z$-embedding
HTML articles powered by AMS MathViewer
- by Kwangho Choiy
- Proc. Amer. Math. Soc. 149 (2021), 2841-2850
- DOI: https://doi.org/10.1090/proc/15426
- Published electronically: April 29, 2021
- PDF | Request permission
Abstract:
We prove that given a pseudo-$z$-embedding two Knapp-Stein $R$-groups are isomorphic and their 2-cocycles are identical.References
- James Arthur, On elliptic tempered characters, Acta Math. 171 (1993), no.Β 1, 73β138. MR 1237898, DOI 10.1007/BF02392767
- Mahdi Asgari and Kwangho Choiy, The local Langlands conjecture for $p$-adic $\rm GSpin_4$, $\rm GSpin_6$, and their inner forms, Forum Math. 29 (2017), no.Β 6, 1261β1290. MR 3719299, DOI 10.1515/forum-2016-0213
- Dubravka Ban, Kwangho Choiy, and David Goldberg, $R$-group and multiplicity in restriction for unitary principal series of GSpin and Spin, Geometry, algebra, number theory, and their information technology applications, Springer Proc. Math. Stat., vol. 251, Springer, Cham, 2018, pp.Β 59β69. MR 3880383, DOI 10.1007/978-3-319-97379-1_{4}
- Dubravka Ban and Chris Jantzen, Duality and the normalization of standard intertwining operators, Manuscripta Math. 115 (2004), no.Β 4, 401β415. MR 2103658, DOI 10.1007/s00229-004-0504-7
- 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.Β 27β61. MR 546608
- Armand Borel, Linear algebraic groups, 2nd ed., Graduate Texts in Mathematics, vol. 126, Springer-Verlag, New York, 1991. MR 1102012, DOI 10.1007/978-1-4612-0941-6
- Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 672956
- Kuok Fai Chao and Wen-Wei Li, Dual $R$-groups of the inner forms of $\textrm {SL}(N)$, Pacific J. Math. 267 (2014), no.Β 1, 35β90. MR 3163476, DOI 10.2140/pjm.2014.267.35
- K. Choiy and D. Goldberg, Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups, Bull. Iranian Math. Soc. 43 (2017), no.Β 4, 117β141. MR 3711825
- Kwangho Choiy, Transfer of Plancherel measures for unitary supercuspidal representations between $p$-adic inner forms, Canad. J. Math. 66 (2014), no.Β 3, 566β595. MR 3194161, DOI 10.4153/CJM-2012-063-1
- Kwangho Choiy, The local Langlands conjecture for the $p$-adic inner form of $\rm Sp_4$, Int. Math. Res. Not. IMRN 6 (2017), 1830β1889. MR 3658185, DOI 10.1093/imrn/rnw043
- Kwangho Choiy, On multiplicity in restriction of tempered representations of $p$-adic groups, Math. Z. 291 (2019), no.Β 1-2, 449β471. MR 3936078, DOI 10.1007/s00209-018-2091-4
- Kwangho Choiy and David Goldberg, Transfer of $R$-groups between $p$-adic inner forms of $SL_n$, Manuscripta Math. 146 (2015), no.Β 1-2, 125β152. MR 3294420, DOI 10.1007/s00229-014-0689-3
- Kwangho Choiy and David Goldberg, Invariance of $R$-groups between $p$-adic inner forms of quasi-split classical groups, Trans. Amer. Math. Soc. 368 (2016), no.Β 2, 1387β1410. MR 3430367, DOI 10.1090/tran/6485
- A. H. Clifford, Representations induced in an invariant subgroup, Ann. of Math. (2) 38 (1937), no.Β 3, 533β550. MR 1503352, DOI 10.2307/1968599
- Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. I, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1981. With applications to finite groups and orders. MR 632548
- S. S. Gelbart and A. W. Knapp, $L$-indistinguishability and $R$ groups for the special linear group, Adv. in Math. 43 (1982), no.Β 2, 101β121. MR 644669, DOI 10.1016/0001-8708(82)90030-5
- David Goldberg, Reducibility of induced representations for $\textrm {Sp}(2n)$ and $\textrm {SO}(n)$, Amer. J. Math. 116 (1994), no.Β 5, 1101β1151. MR 1296726, DOI 10.2307/2374942
- David Goldberg, Reducibility for $\textrm {SU}_n$ and generic elliptic representations, Canad. J. Math. 58 (2006), no.Β 2, 344β361. MR 2209282, DOI 10.4153/CJM-2006-014-6
- Kaoru Hiraga and Hiroshi Saito, On $L$-packets for inner forms of $SL_n$, Mem. Amer. Math. Soc. 215 (2012), no.Β 1013, vi+97. MR 2918491, DOI 10.1090/S0065-9266-2011-00642-8
- Gordon James and Martin Liebeck, Representations and characters of groups, 2nd ed., Cambridge University Press, New York, 2001. MR 1864147, DOI 10.1017/CBO9780511814532
- Tasho Kaletha, Rigid inner forms vs isocrystals, J. Eur. Math. Soc. (JEMS) 20 (2018), no.Β 1, 61β101. MR 3743236, DOI 10.4171/JEMS/759
- C. David Keys, $L$-indistinguishability and $R$-groups for quasisplit groups: unitary groups in even dimension, Ann. Sci. Γcole Norm. Sup. (4) 20 (1987), no.Β 1, 31β64. MR 892141
- A. W. Knapp and E. M. Stein, Irreducibility theorems for the principal series, Conference on Harmonic Analysis (Univ. Maryland, College Park, Md., 1971), Lecture Notes in Math., Vol. 266, Springer, Berlin, 1972, pp.Β 197β214. MR 0422512
- Allan J. Silberger, The Knapp-Stein dimension theorem for $p$-adic groups, Proc. Amer. Math. Soc. 68 (1978), no.Β 2, 243β246. MR 492091, DOI 10.1090/S0002-9939-1978-0492091-5
- Allan J. Silberger, Correction: βThe Knapp-Stein dimension theorem for $p$-adic groupsβ [Proc. Amer. Math. Soc. 68 (1978), no. 2, 243β246; MR 58 #11245], Proc. Amer. Math. Soc. 76 (1979), no.Β 1, 169β170. MR 534411, DOI 10.1090/S0002-9939-1979-0534411-X
- T. A. Springer, Linear algebraic groups, 2nd ed., Progress in Mathematics, vol. 9, BirkhΓ€user Boston, Inc., Boston, MA, 1998. MR 1642713, DOI 10.1007/978-0-8176-4840-4
- Marko TadiΔ, Notes on representations of non-Archimedean $\textrm {SL}(n)$, Pacific J. Math. 152 (1992), no.Β 2, 375β396. MR 1141803
Bibliographic Information
- Kwangho Choiy
- Affiliation: School of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, Illinois 62901-4408
- MR Author ID: 1060574
- Email: kchoiy@siu.edu
- Received by editor(s): April 29, 2019
- Received by editor(s) in revised form: November 23, 2020
- Published electronically: April 29, 2021
- Communicated by: Benjamin Brubaker
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 2841-2850
- MSC (2020): Primary 11F70; Secondary 22E50, 22E35
- DOI: https://doi.org/10.1090/proc/15426
- MathSciNet review: 4257798