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Stable-Limit Non-Symmetric Macdonald Functions in Type A

Student-Run Research Seminar

Speaker: Milo Bechtloff Weising, UC Davis
Location: 2112 MSB
Start time: Thu, Jun 1 2023, 12:00PM

Non-symmetric Macdonald polynomials have an important role in the representation theory of double affine Hecke algebras. These special polynomials give a basis for the standard DAHA representation consisting of weight vectors for the classical Cherednik operators and exhibit many interesting combinatorial properties related to affine Weyl groups. I will discuss a natural extension of these polynomials to the setting of the stable-limit DAHA of Bogdan Ion and Dongyu Wu. In this case we will obtain a basis for the standard stable-limit DAHA representation consisting of weight vectors for the limit Cherednik operators which exhibit combinatorial properties akin to their finite variable counterparts with some interesting differences. Along the way I will give a brief introduction to DAHA, almost symmetric functions, stable-limit convergence, and to some of the combinatorics associated with classical non-symmetric Macdonald polynomials.

Pizza at 11:50am