The University of Illinois Algebra-Geometry-Combinatorics
Seminar |
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Classical determinantal varieties carry a natural action of the general linear group. Their coordinate rings therefore can be decomposed into irreducibles, and this decomposition can be computed via the RSK algorithm. Matrix Schubert varieties [Fulton '92], generalizations of classical determinantal varieties appearing in Schubert calculus, do not usually carry actions of the general linear group; they do, however, carry natural Levi actions. We give a general combinatorial rule, a "filtered" generalization of the RSK algorithm, for computing the decomposition of the coordinate rings of matrix Schubert varieties (and, more generally, "bicrystalline" varieties) into irreducible Levi representations. This talk will focus particularly on the relationship of filteredRSK with the classical Cauchy identity, the basis of standard bitableau, and the standard monomial basis. This is joint work with Ada Stelzer and Alexander Yong.
The seminar co-organizers are Ian Cavey, Andrew Hardt, Shiliang Gao, Elizabeth Kelley, and Alexander Yong.