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Deformed universal characters for classical and affine algebras

Mark Shimozono·Mike Zabrocki
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Abstract

Creation operators are given for the three distinguished bases of the type BCD universal character ring of Koike and Terada yielding an elegant way of treating computations for all three types in a unified manner. Deformed versions of these operators create symmetric function bases whose expansion in the universal character basis, has polynomial coefficients in $q$ with non-negative integer coefficients. We conjecture that these polynomials are one-dimensional sums associated with crystal bases of finite-dimensional modules over quantized affine algebras for all nonexceptional affine types. These polynomials satisfy a Macdonald-type duality.

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Mark Shimozono, Mike Zabrocki. 2004-04-16. Deformed universal characters for classical and affine algebras. https://arxiv.org/abs/math/0404288

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