A Basis for the Symplectic Group Branching Algebra

The symplectic group branching algebra, B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp(2n-2,C) in each irreducible representation of Sp(2n,C). By describing on B an ASL structure, we construct an explicit standard monomial basis of B consisting of Sp(2n-2,C) highest weight vectors. Moreover, B is known to carry a canonical action of the n-fold product SL(2) \times ... \times SL(2), 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 explicit toric variety.Comment: 20 pages, v

On Kostant's partial order on hyperbolic elements

We study Kostant's partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements.Comment: 7 page