Filtering Grassmannian Cohomology via k-Schur Functions

Abstract: This talk concerns the cohomology rings of complex Grassmannians. In $2003$, Reiner and Tudose conjectured the form of the Hilbert series for certain subalgebras of these cohomology rings. We build on their work in two ways. First, we conjecture two natural bases for these subalgebras that would imply their conjecture using notions from the theory of $k$-Schur functions. Second, we formulate an analogous conjecture for Lagrangian Grassmannians.

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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