Stable-Limit Non-symmetric Macdonald Functions in Type A

Abstract

We construct and study an explicit simultaneous $\mathcal{Y}$ eigenbasis of Ion and Wu's standard representation of the ${}^{+}$stable-limit double affine Hecke algebra for the limit Cherednik operators ${\mathcal{Y}}_i$. This basis arises as a generalization of Cherednik's non-symmetric Macdonald polynomials of type $G{L}_n$. 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.

13 pages