First occurrence indices of tempered representations of metaplectic groups
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- by Ivan Matić
- Proc. Amer. Math. Soc. 144 (2016), 3157-3172
- DOI: https://doi.org/10.1090/proc/12943
- Published electronically: December 15, 2015
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Abstract:
We explicitly determine the first occurrence indices of tempered representations of metaplectic groups over a non-archimedean local field of characteristic zero.References
- James Arthur, The endoscopic classification of representations, American Mathematical Society Colloquium Publications, vol. 61, American Mathematical Society, Providence, RI, 2013. Orthogonal and symplectic groups. MR 3135650, DOI 10.1090/coll/061
- I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive ${\mathfrak {p}}$-adic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441–472. MR 579172, DOI 10.24033/asens.1333
- Wee Teck Gan and Atsushi Ichino, Formal degrees and local theta correspondence, Invent. Math. 195 (2014), no. 3, 509–672. MR 3166215, DOI 10.1007/s00222-013-0460-5
- Wee Teck Gan and Gordan Savin, Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence, Compos. Math. 148 (2012), no. 6, 1655–1694. MR 2999299, DOI 10.1112/S0010437X12000486
- Wee Teck Gan and Shuichiro Takeda, On the Howe duality conjecture in classical theta correspondence, Contemp. Math., to appear, 2015.
- Wee Teck Gan and Shuichiro Takeda, A proof of the Howe duality conjecture, J. Amer. Math. Soc., to appear (2015).
- David Goldberg, Reducibility of induced representations for $\textrm {Sp}(2n)$ and $\textrm {SO}(n)$, Amer. J. Math. 116 (1994), no. 5, 1101–1151. MR 1296726, DOI 10.2307/2374942
- Marcela Hanzer and Goran Muić, Parabolic induction and Jacquet functors for metaplectic groups, J. Algebra 323 (2010), no. 1, 241–260. MR 2564837, DOI 10.1016/j.jalgebra.2009.07.001
- Stephen S. Kudla, On the local theta-correspondence, Invent. Math. 83 (1986), no. 2, 229–255. MR 818351, DOI 10.1007/BF01388961
- Stephen S. Kudla, Notes on the local theta correspondence (lectures at the European School in Group Theory), preprint, available at http://www.math.toronto.edu/~skudla/castle.pdf (1996).
- Erez Lapid, Goran Muić, and Marko Tadić, On the generic unitary dual of quasisplit classical groups, Int. Math. Res. Not. 26 (2004), 1335–1354. MR 2046512, DOI 10.1155/S1073792804132832
- Ivan Matić, Theta lifts of strongly positive discrete series: the case of $(\widetilde \textrm {Sp}(n),O(V))$, Pacific J. Math. 259 (2012), no. 2, 445–471. MR 2988500, DOI 10.2140/pjm.2012.259.445
- Ivan Matić, The conservation relation for discrete series representations of metaplectic groups, Int. Math. Res. Not. IMRN 22 (2013), 5227–5269. MR 3129098, DOI 10.1093/imrn/rns209
- C. Mœglin, Sur la classification des séries discrètes des groupes classiques $p$-adiques: paramètres de Langlands et exhaustivité, J. Eur. Math. Soc. (JEMS) 4 (2002), no. 2, 143–200 (French, with English summary). MR 1913095, DOI 10.1007/s100970100033
- Colette Mœglin, Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands, Automorphic forms and related geometry: assessing the legacy of I. I. Piatetski-Shapiro, Contemp. Math., vol. 614, Amer. Math. Soc., Providence, RI, 2014, pp. 295–336 (French, with English summary). MR 3220932, DOI 10.1090/conm/614/12254
- Colette Mœglin and Marko Tadić, Construction of discrete series for classical $p$-adic groups, J. Amer. Math. Soc. 15 (2002), no. 3, 715–786. MR 1896238, DOI 10.1090/S0894-0347-02-00389-2
- Colette Mœglin, Marie-France Vignéras, and Jean-Loup Waldspurger, Correspondances de Howe sur un corps $p$-adique, Lecture Notes in Mathematics, vol. 1291, Springer-Verlag, Berlin, 1987 (French). MR 1041060, DOI 10.1007/BFb0082712
- Goran Muić, Composition series of generalized principal series; the case of strongly positive discrete series, Israel J. Math. 140 (2004), 157–202. MR 2054843, DOI 10.1007/BF02786631
- Goran Muić, Theta lifts of tempered representations for dual pairs $(\textrm {Sp}_{2n},\textrm {O}(V))$, Canad. J. Math. 60 (2008), no. 6, 1306–1335. MR 2462449, DOI 10.4153/CJM-2008-056-6
- Allan J. Silberger, Special representations of reductive $p$-adic groups are not integrable, Ann. of Math. (2) 111 (1980), no. 3, 571–587. MR 577138, DOI 10.2307/1971110
- Binyong Sun and Chen-Bo Zhu, Conservation relations for local theta correspondence, J. Amer. Math. Soc. 28 (2015), no. 4, 939–983. MR 3369906, DOI 10.1090/S0894-0347-2014-00817-1
- Marko Tadić, Structure arising from induction and Jacquet modules of representations of classical $p$-adic groups, J. Algebra 177 (1995), no. 1, 1–33. MR 1356358, DOI 10.1006/jabr.1995.1284
- Marko Tadić, On tempered and square integrable representations of classical $p$-adic groups, Sci. China Math. 56 (2013), no. 11, 2273–2313. MR 3123571, DOI 10.1007/s11425-013-4667-0
- J.-L. Waldspurger, Démonstration d’une conjecture de dualité de Howe dans le cas $p$-adique, $p\neq 2$, Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part I (Ramat Aviv, 1989) Israel Math. Conf. Proc., vol. 2, Weizmann, Jerusalem, 1990, pp. 267–324 (French). MR 1159105
- A. V. Zelevinsky, Induced representations of reductive ${\mathfrak {p}}$-adic groups. II. On irreducible representations of $\textrm {GL}(n)$, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 165–210. MR 584084, DOI 10.24033/asens.1379
Bibliographic Information
- Ivan Matić
- Affiliation: Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia
- MR Author ID: 779049
- ORCID: 0000-0001-9264-9293
- Email: imatic@mathos.hr
- Received by editor(s): February 15, 2015
- Received by editor(s) in revised form: July 8, 2015, and August 21, 2015
- Published electronically: December 15, 2015
- Communicated by: Pham Huu Tiep
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3157-3172
- MSC (2010): Primary 22E35, 11F27
- DOI: https://doi.org/10.1090/proc/12943
- MathSciNet review: 3487245