A Summation Formula for Macdonald Polynomials
Copyright policy )A Summation Formula for Macdonald Polynomials
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and $q$-Whittaker polynomials.
8 pages
- University of Melbourne Australia
Symmetric functions and generalizations, Hall-Littlewood polynomials, FOS: Physical sciences, \(q\)-Whittaker polynomials, Mathematical Physics (math-ph), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), symmetric Macdonald polynomials, monomial symmetric polynomials, \(q\)-calculus and related topics, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Jack polynomials, Representation Theory (math.RT), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Mathematical Physics, Mathematics - Representation Theory
Symmetric functions and generalizations, Hall-Littlewood polynomials, FOS: Physical sciences, \(q\)-Whittaker polynomials, Mathematical Physics (math-ph), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), symmetric Macdonald polynomials, monomial symmetric polynomials, \(q\)-calculus and related topics, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Jack polynomials, Representation Theory (math.RT), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Mathematical Physics, Mathematics - Representation Theory
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