q-Analogs of symmetric function operators

Details q-Analogs of symmetric function operators q-Analogs of symmetric function operators

2000-08-24

arxiv.org/abs/math/0008188v3

Mathematics

Quantum Algebra

17 pages - minor revisions to appear in Discrete Mathematics issue for LaCIM'2000

Scientific paper

For any homomorphism V on the space of symmetric functions, we introduce an operation which creates a q-analog of V. By giving several examples we demonstrate that this quantization occurs naturally within the theory of symmetric functions. In particular, we show that the Hall-Littlewood symmetric functions are formed by taking this q-analog of the Schur symmetric functions and the Macdonald symmetric functions appear by taking the q-analog of the Hall-Littlewood symmetric functions in the parameter t. This relation is then used to derive recurrences on the Macdonald q,t-Kostka coefficients.

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