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arXiv · 2302.08211

Stable-Limit Non-symmetric Macdonald Functions in Type A

Milo Bechtloff Weising
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Abstract

We construct and study an explicit simultaneous $\mathscr{Y}$ eigenbasis of Ion and Wu's standard representation of the $^+$stable-limit double affine Hecke algebra for the limit Cherednik operators $\mathscr{Y}_i$. 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.

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Milo Bechtloff Weising. 2023-02-16. Stable-Limit Non-symmetric Macdonald Functions in Type A. https://arxiv.org/abs/2302.08211

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