Event
Brendon Rhoades, UCSD
The algebra and geometry of ordered set partitions
For any positive integer $n$, there is a graded $S_n$-module (the coinvariant algebra $R_n$) and an algebraic variety (the flag variety $mathcal{F ell}(n)$) whose representation theoretic and geometric properties are governed by permutations in the symmetric group $S_n$. Given two positive integers $k leq n$, we study a new graded $S_n$-module $R_{n,k}$ and a new variety $X_{n,k}$ whose properties are similarly governed by ordered partitions of the set ${1, 2, dots, n}$ into $k$ blocks. Time permitting, we will discuss extensions of these constructions to other reflection groups as well as the Hecke algebra H_n(q) at generic parameter q and in the specialization q = 0. Joint with Jim Haglund, Jia Huang, Brendan Pawlowski, Travis Scrimshaw, and Mark Shimozono.