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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Derivatives and asymptotics of Whittaker functions
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by Nadir Matringe
Represent. Theory 15 (2011), 646-669
Published electronically: September 26, 2011


Let $F$ be a $p$-adic field and $G_n$ be one of the groups $GL(n,F)$, $GSO(2n-1,F)$, $GSp(2(n-1),F)$, or $GSO(2(n-1),F)$. Using the mirabolic subgroup or analogues of it, and related “derivative” functors, we give an asymptotic expansion of functions in the Whittaker model of generic representations of $G_n$, with respect to a minimal set of characters of subgroups of the maximal torus. Denoting by $Z_n$ the center of $G_n$ and by $N_n$ the unipotent radical of its standard Borel subgroup, we characterize generic representations occurring in $L^2(Z_nN_n\backslash G_n)$ in terms of these characters.

This is related to a conjecture of Lapid and Mao for general split groups, asserting that the generic representations occurring in $L^2(Z_nN_n\backslash G_n)$ are the generic discrete series; we prove it for the group $G_n$.

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Bibliographic Information
  • Nadir Matringe
  • Affiliation: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom
  • Address at time of publication: Laboratoire de Mathématiques et Applications, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962, Futuroscope Chasseneuil Cedex, France
  • Email:
  • Received by editor(s): April 7, 2010
  • Received by editor(s) in revised form: September 12, 2010, and October 6, 2010
  • Published electronically: September 26, 2011
  • Additional Notes: This work was supported by the EPSRC grant EP/G001480/1.
  • © Copyright 2011 American Mathematical Society
  • Journal: Represent. Theory 15 (2011), 646-669
  • MSC (2010): Primary 22E50, 22E35
  • DOI:
  • MathSciNet review: 2833471