A Basis for the Symplectic Group Branching Algebra
نویسنده
چکیده
The symplectic group branching algebra, B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n−2(C) in each finite-dimensional irreducible representation of Sp2n(C). By describing on B an ASL structure, we construct an explicit standard monomial basis of B consisting of Sp2n−2(C) highest weight vectors. Moreover, B is known to carry a canonical action of the n-fold product SL2 × ∙ ∙ ∙ × SL2, and we show that the standard monomial basis is the unique (up to scalar) weight basis associated to this representation. Finally, using the theory of Hibi algebras we describe a deformation of Spec(B) into an explicitly described toric variety.
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