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On q,t-symmetry in Macdonald polynomials and its relation to the n! conjecture

Algebra & Discrete Mathematics

Speaker: Maria Gillespie, UC Davis
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Location: 2112 MSB
Start time: Fri, Nov 18 2016, 2:10PM

We discuss some recent results on q,t-symmetry in Macdonald polynomials and how this may help us understand the Garsia-Haiman bigraded S_n-modules. In particular, the Carlitz bijection is an alternative to the Foata bijection that proves the equidistribution of the `inv' and `maj' statistics on permutations. This bijection can be extended in a way that describes the combinatorics of a certain basis of the Garsia-Procesi modules, which essentially correspond to the q=0 specialization of Macdonald polynomials, and we will present some progress towards extending this correspondence to the general setting.