The correlation functions of vertex operators and Macdonald polynomials

Details The correlation functions of vertex operators and Macdonald polynomials The correlation functions of vertex operators and Macdonald polynomials

2005-12-02

arxiv.org/abs/math/0512064v1

J. Algebr. comb. 25 (2007), 43--56.

Mathematics

Combinatorics

12 pages

Scientific paper

The n-point correlation functions introduced by Bloch and Okounkov have already found several geometric connections and algebraic generalizations. In this Note we formulate a q,t-deformation of this n-point function. The key operator used in our formulation arises from the theory of Macdonald polynomials and affords a vertex operator interpretation. We obtain closed formulas for the n-point functions when n =1,2 in terms of the basic hypergeometric functions. We further generalize the q,t-deformed n-point function to more general vertex operators.

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