Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients

Details Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients

2006-05-26

arxiv.org/abs/math/0605691v1

Mathematics

Representation Theory

Scientific paper

Let K be a complex reductive algebraic group and V a representation of K. Let S denote the ring of polynomials on V. Assume that the action of K on S is multiplicity free. If V_{\lambda} is an irreducible representation of K, let S_{\lambda} denote the corresponding isotypic component of S. Write S_{\lambda} S_{\mu} for the subspace of S spanned by products of S_{\lambda} and S_{\mu}. If V_{\nu} occurs as an irreducible constituent of the tensor product of V_{\lambda} and V_{\mu}, is it true that S_{\nu} is contained in S_{\lambda} S_{\mu}? We investigate this question for representations arising in the context of Hermitian symmetric pairs. We show that the answer is yes in some cases and, using an earlier result of Ruitenburg, that in the remaining classical cases, the answer is yes provided that a conjecture of Stanley on the multiplication of Jack polynomials is true. We also show how the conjecture connects multiplication in the ring S to the usual Littlewood-Richardson rule.

Affiliated with

Also associated with

No associations

Rating

Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-238595