Macdonald Polynomials and Algebraic Integrability
Copyright policy )Macdonald Polynomials and Algebraic Integrability
We construct explicitly non-polynomial eigenfunctions of the difference operators by Macdonald in case $t=q^k$, $k\in{\mathbb Z}$. This leads to a new, more elementary proof of several Macdonald conjectures, first proved by Cherednik. We also establish the algebraic integrability of Macdonald operators at $t=q^k$ ($k\in {\mathbb Z}$), generalizing the result of Etingof and Styrkas. Our approach works uniformly for all root systems including $BC_n$ case and related Koornwinder polynomials. Moreover, we apply it for a certain deformation of $A_n$ root system where the previously known methods do not work.
54 pages
- Department of Mathematical Sciences Loughborough University United Kingdom
- Loughborough University United Kingdom
Mathematics(all), algebraic integrability, Macdonald conjectures, Groups and algebras in quantum theory and relations with integrable systems, deformed Macdonald-Ruijsenaars operator, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Baker-Akhiezer function, Koornwinder operator, Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Macdonald polynomials, Combinatorics (math.CO), Macdonald operators, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
Mathematics(all), algebraic integrability, Macdonald conjectures, Groups and algebras in quantum theory and relations with integrable systems, deformed Macdonald-Ruijsenaars operator, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Baker-Akhiezer function, Koornwinder operator, Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Macdonald polynomials, Combinatorics (math.CO), Macdonald operators, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).36 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!