A generalized RSK correspondence for Schubert calculus of the complete flag varieties
Daoji Huang (University of Minnesota)
Friday, February 3, 2023
4088 East Hall Map
We begin by introducing left and right RSK insertions for Schubert calculus of complete flag varieties. The objects being inserted are certain biwords, the insertion objects are bumpless pipe dreams, and the recording objects are decorated chains in Bruhat order. Unlike in the Grassmannian case, the left and right insertions do not always commute. We give a criterion under which they do commute, which motivates the definition of associative biwords that can be used to give a positive rule for Schubert structure constants in the separated-descent case. We generalize Knuth relations to associative biwords and show some basic properties. Furthermore, we demonstrate that the associative biwords naturally admit the Demazure crystal structure and hence give the Schubert-to-key expansions. Finally, we will briefly discuss hopes and obstacles for these techniques to solve more unknown cases of Schubert product rules, as well as some relevant problems for exploration. This is joint work with Pavlo Pylyavskyy; the part relevant to crystals is also joint with Tianyi Yu.
|Event Type:||Workshop / Seminar|
|Source:||Happening @ Michigan from Department of Mathematics, Combinatorics Seminar - Department of Mathematics|