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Rationality of the generalized binomial coefficients for a multiplicity free action

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  09 April 2009

Chal Benson  and
Gail Ratcliff
Chal Benson
Affiliation:
Department of Mathematics and Computer Science University of Missouri-St. LouisSt. Louis, MO 63121USA e-mail: benson@arch.umsl.edu, ratcliff@arch.umsl.edu
Gail Ratcliff
Affiliation:
Department of Mathematics and Computer Science University of Missouri-St. LouisSt. Louis, MO 63121USA e-mail: benson@arch.umsl.edu, ratcliff@arch.umsl.edu
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Abstract

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Let V be a finite dimensional Hermitian vector space and K be a compact Lie subgroup of U(V) for which th representation of K on C[V] is multiplicity free. One obtains a canonical basis {pα} for the space C [VR]k of K-invariant polynomials on VR and also a basis {q's. The polynomial pα's yields the homogeneous component of highest degree in qα. The coefficient that express the qα's in terms of the pβ's are the generalized binomial coeffficients of Yan. The main result in this paper shows tht these numbers are rational.

MSC classification

Secondary: 20G05: Representation theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 387 - 410
Copyright
Copyright © Australian Mathematical Society 2000

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