Schur function identities, their t-analogs, and k-Schur irreducibility |
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Authors: | Luc Lapointe Jennifer Morse |
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Institution: | a Department of Mathematics and Statistics, McGill University, Montréal, Qué., Canada H3A 2K6 b Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA |
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Abstract: | We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using vertex operators. We study subspaces forming a filtration for the symmetric function space that lends itself to generalizing the theory of Schur functions and also provides a convenient environment for studying the Macdonald polynomials. We use our identities to prove that the vertex operators leave such subspaces invariant. We finish by showing that these operators act trivially on the k-Schur functions, thus leading to a concept of irreducibility for these functions. |
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Keywords: | 05E05 |
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