Wednesday, March 20th, 2019
3:00pm - 3:50pm, in McCormack 01-0421

Kyo Nishiyama

Aoyama Gakuin University & MIT

Robinson-Schensted correspondence for partial permutations and moment maps

Abstract: Robinson-Schensted correspondence (RS correspondence in short) is a combinatorial bijection between permutations and pairs of standard tableaux with the same shape. There are astonishingly many ways of achieving this bijection in different algorithms. In early 70's (published later in 1988), Steinberg found a geometric method to explain this bijection, and at the same time he generalize it to any reductive groups. In this talk, we reconsider his geometric description to get a seemingly new bijection between partial permutations and triplets of a pair of tableaux (with different shapes) and a partition called "core". We can also interpret it by the theory of double flag varieties for symmetric pairs, and get a general frame work for considering those new combinatorial bijections, which reveals an interesting interchange between geometry and combinatorics. The talk is based on the on-going joint work with Lucas Fresse at IECL (France).