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q-Hypergeometric Series and Macdonald Functions
Authors:Naihuan Jing
Institution:(1) Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045-2142
Abstract:We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type 4PHgr3, for which we obtain linear transformation formulas in terms of the Jacobi theta function and the q-Gamma function. The transformation formulas are then used to give the duality formula and a new formula for two-row Macdonald functions in terms of the vertex operators. The Jack polynomials are also treated accordingly.
Keywords:basic hypergeometric function  vertex operator  Macdonald symmetric function  Jack symmetric function
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