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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.

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.

 

On endomorphism algebras of Gelfand-Graev representations
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by Tzu-Jan Li PDF
Represent. Theory 27 (2023), 80-114

Abstract:

For a connected reductive group $G$ defined over $\mathbb {F}_q$ and equipped with the induced Frobenius endomorphism $F$, we study the relation among the following three $\mathbb {Z}$-algebras: (i) the $\mathbb {Z}$-model $\mathsf {E}_G$ of endomorphism algebras of Gelfand-Graev representations of $G^F$; (ii) the Grothendieck group $\mathsf {K}_{G^\ast }$ of the category of representations of $G^{\ast F^\ast }$ over $\overline {\mathbb {F}_q}$ (Deligne-Lusztig dual side); (iii) the ring $\mathsf {B}_{G^\vee }$ of the scheme $(T^\vee /\!\!/ W)^{F^\vee }$ over $\mathbb {Z}$ (Langlands dual side). The comparison between (i) and (iii) is motivated by recent advances in the local Langlands program.
References
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Additional Information
  • Tzu-Jan Li
  • Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche (IMJ-PRG), 4 place Jussieu, 75252 Paris cedex 05, France
  • Email: tzu-jan.li@imj-prg.fr
  • Received by editor(s): December 10, 2021
  • Received by editor(s) in revised form: June 7, 2022, and June 22, 2022
  • Published electronically: April 26, 2023
  • Additional Notes: This project received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754362.
  • © Copyright 2023 Copyright by Tzu-Jan Li
  • Journal: Represent. Theory 27 (2023), 80-114
  • MSC (2020): Primary 20C33
  • DOI: https://doi.org/10.1090/ert/627
  • MathSciNet review: 4580514