Abstract
We show that the centraliser of the maximal compact subgroup of the real groups O ( p , q ) and S p 2 n ( R ) acting on tensors of their standard representation is isomorphic to the level 2 cyclotomic Brauer algebra with certain parameters in C . We also prove that for S p 2 n ( R ) this cyclotomic Brauer algebra is Morita equivalent to a direct sum of walled Brauer algebras.
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