Séminaire Lotharingien de Combinatoire, 89B.56 (2023), 12 pp.

Milo James Bechtloff Weising

Stable-Limit Non-Symmetric Macdonald Functions in Type A

Abstract. We construct and study an explicit simultaneous Y eigenbasis of Ion and Wu's standard representation of the ⁺stable-limit double affine Hecke algebra for the limit Cherednik operators Y_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.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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