On Donkin's Tilting Module Conjecture III: New generic lower bounds

Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper the authors consider four questions of primary interest for the representation theory of reductive algebraic groups: (i) Donkin's Tilting Module Conjecture, (ii) the Humphreys-Verma Question, (iii) whether Str⊗L(λ) is a tilting module for L(λ) an irreducible representation of pr-restricted highest weight, and (iv) whether ExtG11(L(λ),L(μ))(−1) is a tilting module where L(λ) and L(μ) have p-restricted highest weight. The authors establish affirmative answers to each of these questions with a new uniform bound, namely p≥2h−4 where h is the Coxeter number. Notably, this verifies these statements for infinitely many more cases. Later in the paper, questions (i)-(iv) are considered for rank two groups where there are counterexamples (for small primes) to these questions.

Original languageEnglish
Pages (from-to)95-109
Number of pages15
JournalJournal of Algebra
Volume655
DOIs
StatePublished - Oct 1 2024

Scopus Subject Areas

  • Algebra and Number Theory

Keywords

  • Cohomology
  • Representations of algebraic groups
  • Tilting modules

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