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Rhombic staircase tableaux and Koornwinder polynomials

Algebra & Discrete Mathematics

Speaker: Sylvie Corteel, UC Berkeley
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Location: 2112 MSB
Start time: Tue, Feb 27 2024, 1:10PM

We give a combinatorial formula for a certain class of Koornwinder polynomials indexed by a partition $\lambda$, also known as Macdonald polynomials of type $\tilde{C}_N$ when $\lambda=(1,\ldots ,1,0,\ldots,0)$ and some non symmetric analogue that we call "open boundary ASEP polynomials". Our formulas are in terms of rhombic staircase tableaux, certain tableaux that we introduced in previous work to give a formula for the stationary distribution of the two-species asymmetric simple exclusion process (ASEP) on a line with open boundaries. This talk will not require any prior knowledge. This is joint work with Olya Mandelshtam and Lauren Williams.