Morita equivalence for blocks of Hecke algebras of type \(B\)
type: Item
instance of: scholarly article
title: Morita equivalence for blocks of Hecke algebras of type \(B\)
zbMATH Open document ID: 0935.20004
author: Thomas Jost
published in: Journal of Algebra
publication date: 2000-05-03T00:00:00Z
review text: The author continues his work [from J. Algebra 194, No. 1, 201-223 (1997; Zbl 0883.20009) and Manuscr. Math. 91, No. 1, 121-144 (1996; Zbl 0896.20009)] and shows that given a pair \(w=(w_1,w_2)\) of nonnegative integers, a complete discrete valuation ring \(R\) and parameters \(q\), \(Q\) in \(R\), there is only a finite number of Morita equivalence classes of blocks of Hecke algebras of type \(B\) over \(R\) with parameters \(q\), \(Q\) whose weight tuple is \(w\). Let \(F\) denote the residue class field of \(R\). The notion of a combinatorial \((w:k)\)-pair is introduced which is then used to define \((w_i:k_i)\)-pairs of blocks \(B\), \(\overline B\) of Hecke algebras \(H_F(W_n)\) and \(H_F(W_{n-k_i})\) of type \(B\) over \(F\), respectively. A bijection between the simple modules in \(B\) and \(\overline B\) is set up, and from this it is deduced that the blocks \(B\) and \(\overline B\) have the same decomposition matrices and hence also the same Cartan matrices. It is then shown that the blocks \(B\) and \(\overline B\) are Morita equivalent by setting up a pair of functors \(G\), \(G'\) between mod-\(B\) and mod-\(\overline B\). As a consequence the main result mentioned in the beginning is proved.
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1340605
zbMATH Keywords: Morita equivalences
zbMATH Keywords: blocks of Hecke algebras
zbMATH Keywords: weights
zbMATH Keywords: simple modules
zbMATH Keywords: decomposition matrices
zbMATH Keywords: Cartan matrices
MaRDI profile type: Publication
full work available at URL: jabr.1998.7802
OpenAlex ID: W1992490628
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DOI: 10.1006/JABR.1998.7802
description: scientific article; zbMATH DE number 1340605