Algebra and Combinatorics Seminar
Date: January 27, 2023
Time: 3:00PM - 3:50PM
Location: BLOC 302
Speaker: Ayah Almousa, University of Minnesota
Title: GL-equivariant resolutions over Veronese subrings
Abstract: We construct explicit GL-equivariant minimal free resolutions of certain (truncations of) modules of relative invariants over Veronese subrings in arbitrary characteristic. The free modules in the resolution correspond to certain skew Schur modules associated to "ribbon" or "skew-hook" diagrams, and the differentials at each step are surprisingly uniform. We then utilize the uniformity of these resolutions to explicitly compute information about tensor products, Hom, and Tor between these modules and show that they also have rather simple descriptions in terms of ribbon skew-Schur modules. I will emphasize the hidden role of symmetric function theory in detecting the answer to this question and guiding our intuition to build new tools to prove our results in arbitrary characteristic. This is joint work with Mike Perlman, Sasha Pevzner, Vic Reiner, and Keller VandeBogert.