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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Coxeter combinatorics for sum formulas in the representation theory of algebraic groups
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by Jonathan Gruber PDF
Represent. Theory 26 (2022), 68-93 Request permission


Let $G$ be a simple algebraic group over an algebraically closed field $\mathbb {F}$ of characteristic $p \geq h$, the Coxeter number of $G$. We observe an easy ‘recursion formula’ for computing the Jantzen sum formula of a Weyl module with $p$-regular highest weight. We also discuss a ‘duality formula’ that relates the Jantzen sum formula to Andersen’s sum formula for tilting filtrations and we give two different representation theoretic explanations of the recursion formula. As a corollary, we also obtain an upper bound on the length of the Jantzen filtration of a Weyl module with $p$-regular highest weight in terms of the length of the Jantzen filtration of a Weyl module with highest weight in an adjacent alcove.
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Additional Information
  • Jonathan Gruber
  • Affiliation: École Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland
  • MR Author ID: 1425592
  • ORCID: 0000-0001-5975-8041
  • Email:
  • Received by editor(s): July 7, 2021
  • Received by editor(s) in revised form: August 20, 2021
  • Published electronically: March 2, 2022
  • Additional Notes: This work was supported by the Swiss National Science Foundation under grant number FNS 200020_175571.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 68-93
  • MSC (2020): Primary 20G05
  • DOI:
  • MathSciNet review: 4388551