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On the square root of the centre of the Hecke algebra of type A

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Andrew Francis  and
Lenny Jones
Andrew Francis
Affiliation:
School of Computing and Mathematics Univeristy of Western SydneyNSW 1797Australia e-mail: a.francis@uws.edu.au
Lenny Jones
Affiliation:
Department of Mathematics Shippenburg UniversityPennsylvaniaUSA e-mail: lkjone@ship.edu
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Abstract

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In this paper we investigate non-central elements of the Iwahori-Hecke algebra of the symmetric group whose squares are central. In particular, we describe a commutative subalgebra generated by certain non-central square roots of central elements, and the generic existence of a rank-three submodule of the Hecke algebra contained in the square root of the centre, but not in the centre. The generators for this commutative subalgebra include the longest word and elements related to trivial and sign characters of the Hecke algebra. We find elegant expressions for the squares of such generators in terms of both the minimal basis of the centre and the elementary symmetric functions of Murphy elements.

MSC classification

Secondary: 20C08: Hecke algebras and their representations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 2 , April 2007 , pp. 209 - 220
Copyright
Copyright © Australian Mathematical Society 2007

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