Deformed universal characters for classical and affine algebras

Details Deformed universal characters for classical and affine algebras Deformed universal characters for classical and affine algebras

2004-04-16

arxiv.org/abs/math/0404288v1

Mathematics

Combinatorics

29 pages

Scientific paper

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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