Abstract:
When a reductive group \$G\$ acts on an embedded projective variety \$X\$, the associated coordinate ring \$\mathbf C[X]\$ is a \$G\$-representation. The data of this representation may be recorded directly as the \$G\$-equivariant Hilbert series of \$\mathbf C[X]\$, or more compactly as its \$K\$-polynomial or twisted \$K\$-polynomial (which are connected to the minimal free resolution and multidegree of \$\mathbf C[X]\$ respectively). Non-cancellative combinatorial rules for the coefficients in all three polynomials are therefore desirable. In this talk we focus on determinantal varieties, where the combinatorics of pipe dreams and the Robinson-Schensted-Knuth correspondence naturally arise. We present joint work with Abigail Price and Alexander Yong describing the \$G\$-equivariant Hilbert series of generalized determinantal varieties, along with open problems and directions for future research.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974