Title: A new shifted Littlewood-Richardson rule
| Speaker: | Santiago Estupinan |
| Affiliation: | University of Waterloo |
| Location: | MC 5479 |
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.
Abstract: As Littlewood-Richardson rules compute linear representation theory of symmetric groups and cohomology of ordinary Grassmannians, shifted Littlewood-Richardson rules compute analogous projective representation theory of symmetric groups and cohomology of orthogonal Grassmannians. The first shifted Littlewood-Richardson rule is due to Stembridge (1989), building on a natural generalization by Sagan and Worley (1979/1984) of the jeu de taquin algorithm to shifted Young tableaux. We give a new shifted Littlewood-Richardson rule that requires consideration of fewer tableaux than Stembridge's rule and appears to involve an easier check on each. Our rule derives from applying old ideas of Lascoux and Schützenberger (1981) to the study of Haiman's mixed insertion (1989) and Serrano's shifted plactic monoid (2010). (Joint work with Oliver Pechenik).