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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.
|Uncontrolled Keywords:||Brauer algebras, representation theory, CENTRALIZER ALGEBRAS, CELLULAR ALGEBRAS, SCHUR ALGEBRAS, REPRESENTATIONS, CHARACTERS|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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