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Journal of the London Mathematical Society Advance Access originally published online on August 9, 2009
Journal of the London Mathematical Society 2009 80(2):471-494; doi:10.1112/jlms/jdp039
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© 2009 London Mathematical Society

A geometric characterisation of the blocks of the Brauer algebra

Anton Cox

Centre for Mathematical Science
City University
Northampton Square
London
EC1V 0HB
United Kingdom

Maud De Visscher

Centre for Mathematical Science
City University
Northampton Square
London
EC1V 0HB
United Kingdom
M.Devisscher@city.ac.uk

Paul Martin

Department of Pure Mathematics
University of Leeds
Leeds
LS2 9JT
United Kingdom
ppmartin@maths.leeds.ac.uk

We give a geometric description of the blocks of the Brauer algebra in characteristic zero as orbits of the Weyl group of type Dn. We show how the corresponding affine Weyl group controls the block decomposition of the Brauer algebra in positive characteristic, with orbits corresponding to unions of blocks.

2000 Mathematics Subject Classification 20G05.

Received March 30, 2007; revised February 18, 2009; published online August 9, 2009.


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