Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - June 2012 - Volume 55, Issue 02  

Research Article

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

Kevin McGertya1

a1 Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford OX1 3LB, UK (kevin.mcgerty@maths.ox.ac.uk)

Abstract

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.

(Received October 03 2010)

Keywords

  • affine and cyclotomic Hecke algebras;
  • centres;
  • representation theory;
  • algebraic theory

2010 Mathematics subject classification

  • Primary 20C08;
  • Secondary 17B10