On q,t-symmetry in Macdonald polynomials and its relation to the n! conjectureAlgebra & Discrete Mathematics
|Speaker:||Maria Gillespie, UC Davis|
|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.