Recognition: unknown
(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula
classification
q-alg
math.QA
keywords
polynomialsmacdonaldshiftedrepresentationcombinatorialformulaintegralcontext
read the original abstract
We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a $q$-integral representation and a combinatorial formula. Our main tool is a $q$-integral representation for ordinary Macdonald polynomials. We also discuss duality for shifted Macdonald polynomials and Jack degeneration of these polynomials.
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