English

Deformed universal characters for classical and affine algebras

Combinatorics 2007-05-23 v1 Quantum Algebra

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 qq 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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Cite

@article{arxiv.math/0404288,
  title  = {Deformed universal characters for classical and affine algebras},
  author = {Mark Shimozono and Mike Zabrocki},
  journal= {arXiv preprint arXiv:math/0404288},
  year   = {2007}
}

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29 pages