On l-parabolic Hecke algebras of symmetric groups

DOI10.1007/S13366-020-00522-7arXiv2001.02401MaRDI QIDQ6332498

Karin Erdmann

Publication date: 8 January 2020

Abstract: Let $H=H_q(n)$ be the Hecke algebra of the symmetric group of degree n, over a field of arbitrary characteristic, and where q is a primitive l-th root of unity in $K$. Let $H_{ho}$ be an l-parabolic subalgebra of $H$. We give an elementary explicit construction for the basic algebra of a non-simple block of $H_{ho}$. We also discuss homological properties of $H_{ho}$-modules, in particular existence of varieties for modules, and some consequences.

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Finite rings and finite-dimensional associative algebras (16P10) Representations of finite symmetric groups (20C30) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of associative Artinian rings (16G10) Artinian rings and modules (associative rings and algebras) (16P20)

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