Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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.

 

Dimensions of modular irreducible representations of semisimple Lie algebras
HTML articles powered by AMS MathViewer

by Roman Bezrukavnikov and Ivan Losev
J. Amer. Math. Soc. 36 (2023), 1235-1304
DOI: https://doi.org/10.1090/jams/1017
Published electronically: March 16, 2023

Abstract:

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with respect to a group whose connected component is a torus. Character computation is done in two steps. First, we treat the case of distinguished $p$-characters: those that are not contained in a proper Levi. Here we essentially show that the category of equivariant modules we consider is a cell quotient of an affine parabolic category $\mathcal {O}$. For this, we prove an equivalence between two categorifications of a parabolically induced module over the affine Hecke algebra conjectured by the first named author. For the general nilpotent $p$-character, we get character formulas by explicitly computing the duality operator on a suitable equivariant K-group.
References
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2020): 17B20, 17B35, 17B50
  • Retrieve articles in all journals with MSC (2020): 17B20, 17B35, 17B50
Bibliographic Information
  • Roman Bezrukavnikov
  • Affiliation: Department of Mathematics, MIT, Cambridge, Massachusetts 02139
  • MR Author ID: 347192
  • Email: bezrukav@math.mit.edu
  • Ivan Losev
  • Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06511
  • MR Author ID: 775766
  • Email: ivan.loseu@yale.edu
  • Received by editor(s): November 5, 2020
  • Received by editor(s) in revised form: March 22, 2022, and August 30, 2022
  • Published electronically: March 16, 2023
  • Additional Notes: The first author was partially supported by the NSF under grant DMS-1601953. The second author was partially supported by the NSF under grant DMS-1501558.
  • © Copyright 2023 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 36 (2023), 1235-1304
  • MSC (2020): Primary 17B20, 17B35, 17B50
  • DOI: https://doi.org/10.1090/jams/1017
  • MathSciNet review: 4618958