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On the centre of the cyclotomic Hecke algebra of G(m, 1, 2)

Part of: Lie algebras and Lie superalgebras Representation theory of groups

Published online by Cambridge University Press:  12 April 2012

Kevin McGerty
Kevin McGerty
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford OX1 3LB, UK (kevin.mcgerty@maths.ox.ac.uk)
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Abstract

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We compute the centre of the cyclotomic Hecke algebra attached to G(m, 1, 2) and show that if q ≠ 1, it is equal to the image of the centre of the affine Hecke algebra Haff2. We also briefly discuss what is known about the relation between the centre of an arbitrary cyclotomic Hecke algebra and the centre of the affine Hecke algebra of type A.

Keywords

affine and cyclotomic Hecke algebrascentresrepresentation theoryalgebraic theory

MSC classification

Secondary: 20C08: Hecke algebras and their representations 17B10: Representations, algebraic theory (weights)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 497 - 506
Copyright
Copyright © Edinburgh Mathematical Society 2012

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