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- W4384261769 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 $GL$. We utilize links between $^+$stable-limit double affine Hecke algebra theory of Ion-Wu and the double Dyck path algebra of Carlsson-Mellit that arose in their proof of the Shuffle Conjecture. As a consequence, the spectral theory for the limit Cherednik operators is understood. The symmetric functions comprise the zero weight space. We introduce one extra operator that commutes with the $mathscr{Y}_i$ action and dramatically refines the weight spaces to now be one-dimensional. This operator, up to a change of variables, gives an extension of Haiman's operator $Delta'$ from $Lambda$ to $mathscr{P}_{as}^{+}.$ Additionally, we develop another method to build this weight basis using limits of trivial idempotents." @default.
- W4384261769 created "2023-07-14" @default.
- W4384261769 creator A5092467234 @default.
- W4384261769 date "2023-07-11" @default.
- W4384261769 modified "2023-09-25" @default.
- W4384261769 title "Stable-Limit Non-symmetric Macdonald Functions" @default.
- W4384261769 doi "https://doi.org/10.48550/arxiv.2307.05864" @default.
- W4384261769 hasPublicationYear "2023" @default.
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