On CRDAHA and finite general linear and unitary groups
Bhama Srinivasan

TL;DR
This paper explores the relationship between Lusztig induction in finite groups and parabolic induction in affine Hecke algebras, providing new insights into modular representation theory and explaining existing bijection results.
Contribution
It establishes a novel connection between induction operators in finite groups and affine Hecke algebras, advancing understanding of modular representations.
Findings
Connected Lusztig induction with affine Hecke algebra induction
Explained Broué-Malle-Michel bijection
Derived results on modular decomposition numbers
Abstract
We show a connection between Lusztig induction operators in finite general linear and unitary groups and parabolic induction in cyclotomic rational double affine Hecke algebras. Two applications are given: an explanation of a bijection result of Brou\'e, Malle and Michel, and some results on modular decomposition numbers of finite general groups.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics
