Hall-Littlewood polynomials and a Hecke action on ordered set partitions

Huang, Jia; Rhoades, Brendon; Scrimshaw, Travis

doi:10.1090/proc/14157

Hall-Littlewood polynomials and a Hecke action on ordered set partitions
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by Jia Huang, Brendon Rhoades and Travis Scrimshaw PDF

Proc. Amer. Math. Soc. 147 (2019), 1839-1850 Request permission

Abstract:

We construct an action of the Hecke algebra $H_n(q)$ on a quotient of the polynomial ring $F[x_1, \dots , x_n]$, where $F =\mathbb {Q}(q)$. The dimension of our quotient ring is the number of $k$-block ordered set partitions of $\{1, 2, \dots , n\}$. This gives a quantum analog of a construction of Haglund–Rhoades–Shimozono and interpolates between their result at $q = 1$ and work of Huang–Rhoades at $q = 0$.

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