Affiliation:
1. Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Abstract
Abstract
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a finite field, with the spherical functions being sent to Macdonald polynomials with parameters $(q,q^2)$. An analogue of parabolic induction is interpreted as a certain multiplication of symmetric functions. Applications are given to Schur positivity of skew Macdonald polynomials with parameters $(q,q^2)$ as well as combinatorial formulas for spherical function values.
Funder
Natural Sciences and Engineering Research Council of Canada
Publisher
Oxford University Press (OUP)
Cited by
1 articles.
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