On the blocks of the walled Brauer algebra

Details On the blocks of the walled Brauer algebra On the blocks of the walled Brauer algebra

2007-09-06

arxiv.org/abs/0709.0851v1

Mathematics

Representation Theory

40 pages, 16 figures

Scientific paper

We determine the blocks of the walled Brauer algebra in characteristic zero.
These can be described in terms of orbits of the action of a Weyl group of type
$A$ on a certain set of weights. In positive characteristic we give a linkage
principle in terms of orbits of the corresponding affine Weyl group. We also
classify the semisimple walled Brauer algebras in all characteristics.

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