Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Langlands parameters associated to special maximal parahoric spherical representations
HTML articles powered by AMS MathViewer

by Manish Mishra PDF
Proc. Amer. Math. Soc. 143 (2015), 1933-1941 Request permission

Abstract:

We describe the image, under the local Langlands correspondence for tori, of the characters of a torus which are trivial on its Iwahori subgroup. Let $k$ be a non-archimedian local field. Let $\boldsymbol {G}$ be a connected reductive group defined over $k$, which is quasi-split and split over a tamely ramified extension. Let $K$ be a special maximal parahoric subgroup of $\boldsymbol {G}(k)$. To the class of representations of $\boldsymbol {G}(k)$ having a non-zero vector fixed under $K$, we establish a bijection, in a natural way, with the twisted semisimple conjugacy classes of the inertia fixed subgroup of the dual group $\hat {\boldsymbol {G}}$. These results generalize the well known classical results to the ramified case.
References
  • 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
  • P. Cartier, Representations of $p$-adic groups: a survey, 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. 111–155. MR 546593
  • T. Haines, The stable Bernstein center and test functions for Shimura varieties, arXiv:1304.6293. To appear in the proceedings for the London Mathematical Society - EPSRC Durham Symposium on Automorphic Forms and Galois Representations, Durham, July 18-28, 2011.
  • Thomas J. Haines and Sean Rostami, The Satake isomorphism for special maximal parahoric Hecke algebras, Represent. Theory 14 (2010), 264–284. MR 2602034, DOI 10.1090/S1088-4165-10-00370-5
  • T. Kaletha, Epelagic $L$-packets and rectifying characters, arXiv:1209.1720
  • Robert E. Kottwitz, Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), no. 3, 611–650. MR 757954, DOI 10.1215/S0012-7094-84-05129-9
  • Robert E. Kottwitz, Isocrystals with additional structure. II, Compositio Math. 109 (1997), no. 3, 255–339. MR 1485921, DOI 10.1023/A:1000102604688
  • Robert E. Kottwitz and Diana Shelstad, Foundations of twisted endoscopy, Astérisque 255 (1999), vi+190 (English, with English and French summaries). MR 1687096
  • Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728
  • Rainer Weissauer, Endoscopy for $\textrm {GSp}(4)$ and the cohomology of Siegel modular threefolds, Lecture Notes in Mathematics, vol. 1968, Springer-Verlag, Berlin, 2009. MR 2498783, DOI 10.1007/978-3-540-89306-6
  • Jiu-Kang Yu, On the local Langlands correspondence for tori, Ottawa lectures on admissible representations of reductive $p$-adic groups, Fields Inst. Monogr., vol. 26, Amer. Math. Soc., Providence, RI, 2009, pp. 177–183. MR 2508725, DOI 10.1090/fim/026/07
  • Xinwen Zhu, The geometric Satake correspondence for ramified groups, arXiv:1107.5762
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11R39, 20G05, 22E50
  • Retrieve articles in all journals with MSC (2010): 11R39, 20G05, 22E50
Additional Information
  • Manish Mishra
  • Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
  • Email: mmishra@math.huji.ac.il
  • Received by editor(s): April 20, 2013
  • Received by editor(s) in revised form: October 15, 2013, and October 25, 2013
  • Published electronically: December 19, 2014
  • Communicated by: Pham Huu Tiep
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 1933-1941
  • MSC (2010): Primary 11R39, 20G05, 22E50
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12392-6
  • MathSciNet review: 3314103