c-functions and Macdonald polynomials
Copyright policy )c-functions and Macdonald polynomials
This is a paper about $c$-functions and Macdonald polynomials. There are $c$-function formulas for $E$-expansions of $P_λ$ and $A_{λ+ρ}$, principal specializations of $P_λ$ and $E_μ$, for Macdonald's constant term formulas, and for the norms of Macdonald polynomials. Most of these follow from the creation formulas for Macdonald polynomials, providing alternative proofs to several results from Macdonald (2003). In addition, we prove the Boson-Fermion correspondence in the Macdonald polynomial setting and the Weyl character formula for Macdonald polynomials.
- University of Melbourne Australia
Symmetric functions and generalizations, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, symmetric functions, 05E05 (Primary), 33D52 (Secondary), Combinatorics (math.CO), Representation Theory (math.RT), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Hecke algebras, Mathematics - Representation Theory
Symmetric functions and generalizations, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, symmetric functions, 05E05 (Primary), 33D52 (Secondary), Combinatorics (math.CO), Representation Theory (math.RT), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Hecke algebras, Mathematics - Representation Theory
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