Stable-Limit Non-symmetric Macdonald Functions in Type A

2023/02/16 by Milo Bechtloff Weising, Weising, Milo Bechtloff
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2302.08211

Abstract

We construct and study an explicit simultaneous \mathscrY eigenbasis of Ion and Wu's standard representation of the ⁺stable-limit double affine Hecke algebra for the limit Cherednik operators \mathscrY_i. This basis arises as a generalization of Cherednik's non-symmetric Macdonald polynomials of type GL_n. We utilize links between ⁺stable-limit double affine Hecke algebra theory of Ion and Wu and the double Dyck path algebra of Carlsson and Mellit that arose in their proof of the Shuffle Conjecture. As a consequence, the spectral theory for the limit Cherednik operators is understood.

Related

• Stable-Limit Non-symmetric Macdonald Functions
• Higher Rank Macdonald Polynomials
• Vector valued Macdonald polynomials
• Nonsymmetric Macdonald polynomials, Demazure modules and PBW filtration
• Affine Hecke algebras and symmetric quasi-polynomial duality