Matrices for affine Hecke modules
type: Item
instance of: scholarly article
title: Matrices for affine Hecke modules
zbMATH Open document ID: 0979.20008
author: Mark Reeder
published in: Journal of Algebra
publication date: 2002-02-12T00:00:00Z
review text: Let \(H\) be the affine Hecke algebra associated with a reductive Lie group \(G\). Then \(H\) is generated by two subalgebras \(H_0\) and \(A\), where \(A\) is the coordinate ring of a complex torus \(T\), which is a maximal torus in \(G\), and \(H_0\) is generated by operators \(T_s\), where \(s\) runs over a fixed set \(\Sigma\) of simple reflections in the Weyl group \(W\) of \(G\), satisfying the usual braid relations along with the relation \((T_s-q_s)(T_s+1)=0\) for parameters \(q_s>0\). The restriction of any finite-dimensional \(H\)-module \(E\) to the commutative algebra \(A\) decomposes as \(E=\bigoplus_{\tau\in T}E_\tau\), where \(E_\tau\) is the weight space consisting of the vectors in \(E\) annihilated by some power of the maximal ideal \(m_\tau\) of \(A\). This paper is an extension of an earlier work done by the author [in Forum Math. 9, No. 4, 457-516 (1997; Zbl 0882.22020)]. The main result is an explicit formula for the weight spaces in a simple \(H\)-module with standard singularity. This formula is valid for any parameter set \(\{q_s\}\).
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 1526436
zbMATH Keywords: affine Hecke algebras
zbMATH Keywords: reductive Lie groups
zbMATH Keywords: coordinate rings
zbMATH Keywords: simple reflections
zbMATH Keywords: Weyl groups
zbMATH Keywords: braid relations
zbMATH Keywords: finite-dimensional modules
zbMATH Keywords: weight spaces
reviewed by: Ahmed A. Khammash
MaRDI profile type: Publication
full work available at URL: jabr.1999.8369
OpenAlex ID: W1996821538
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DOI: 10.1006/JABR.1999.8369
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description: scientific article; zbMATH DE number 1526436