Support varieties for Hecke algebras

DOI10.4310/HHA.2019.V21.N2.A5zbMath1480.20037arXiv1712.02755OpenAlexW2963392690WikidataQ128710475 ScholiaQ128710475MaRDI QIDQ2326302

Daniel K. Nakano, Ziqing Xiang

Publication date: 7 October 2019

Published in: Homology, Homotopy and Applications (Search for Journal in Brave)

Abstract: Let ${mathcalH}_q(d)$ be the Iwahori-Hecke algebra for the symmetric group, where $q$ is a primitive $l$th root of unity. In this paper we develop a theory of support varieties which detects natural homological properties such as the complexity of modules. The theory the authors develop has a canonical description in an affine space where computations are tractable. The ideas involve the interplay with the computation of the cohomology ring due to Benson, Erdmann and Mikaelian, the theory of vertices due to Dipper and Du, and branching results for cohomology by Hemmer and Nakano. Calculations of support varieties and vertices are presented for permutation, Young and classes of Specht modules. Furthermore, a discussion of how the authors' results can be extended to other Hecke algebras for other classical groups is presented at the end of the paper.

Full work available at URL: https://arxiv.org/abs/1712.02755

zbMATH Keywords

cohomologyHecke algebrasupport variety

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Representations of finite symmetric groups (20C30) Cohomology of groups (20J06)

Related Items (1)

On \(\ell\)-parabolic Hecke algebras of symmetric groups

This page was built for publication: Support varieties for Hecke algebras