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Schur–Weyl duality for orthogonal groups
 Proceedings of the London Mathematical Society
"... Abstract. We prove Schur–Weyl duality between the Brauer algebra Bn(m) and the orthogonal group Om(K) over an arbitrary infinite field K of odd characteristic. If m is even, we show that each connected component of the orthogonal monoid is a normal variety; this implies that the orthogonal Schur alg ..."
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Abstract. We prove Schur–Weyl duality between the Brauer algebra Bn(m) and the orthogonal group Om(K) over an arbitrary infinite field K of odd characteristic. If m is even, we show that each connected component of the orthogonal monoid is a normal variety; this implies that the orthogonal Schur algebra associated to the identity component is a generalized Schur algebra. As an application of the main result, an explicit and characteristicfree description of the annihilator of ntensor space V ⊗n in the Brauer algebra Bn(m) is also given. 1.
Stability properties for qmultiplicities and branching formulas for representations of the classical groups
, 2000
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On the radical of Brauer algebras
, 2006
"... is known to be nontrivial when the parameter x is an integer subject to certain conditions (with respect to f). In these cases, we display a wide family of elements in the radical, which are explicitly described by means of the diagrams of the usual basis of B (x). The proof is by direct approach f ..."
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is known to be nontrivial when the parameter x is an integer subject to certain conditions (with respect to f). In these cases, we display a wide family of elements in the radical, which are explicitly described by means of the diagrams of the usual basis of B (x). The proof is by direct approach for x = 0, and via Abstract. The radical of the Brauer algebra B (x) f f classical Invariant Theory in the other cases, exploiting then the wellknown representation of Brauer algebras as centralizer algebras of orthogonal or symplectic groups acting on tensor powers of their standard representation. This also gives a great part of the radical of the –modules. We conjecture that these subsets of the radicals (for the algebra and for the modules) actually coincide with the whole radical itself. As an application, we find some more precise results for the module of pointed chord generic irreducible B (x) f diagrams, and for the TemperleyLieb algebra — realised inside B (1)
DIRAC COHOMOLOGY, KCHARACTERS AND BRANCHING Laws
"... Inspired by work of Enright and Willenbring [EW], we prove a generalized Littlewood’s restriction formula in terms of Dirac cohomology. Our approach is to use a character formula of irreducible unitary lowest weight modules instead of the BernsteinGelfandGelfand resolution, and the proof is much ..."
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Inspired by work of Enright and Willenbring [EW], we prove a generalized Littlewood’s restriction formula in terms of Dirac cohomology. Our approach is to use a character formula of irreducible unitary lowest weight modules instead of the BernsteinGelfandGelfand resolution, and the proof is much simpler. We also show that our branching formula is equivalent to the formula of Enright and Willenbring in terms of nilpotent Lie algebra cohomology. This follows from the close relationship between the Dirac cohomology and the corresponding nilpotent Lie algebra cohomology for unitary representations of semisimple Lie groups of Hermitian type, which was established in [HPR].