In their seminal paper on FI-modules, Church, Ellenberg, and Farb introduced a category theoretic interpretation of a phenomenon known as representation stability. However, their approach required computing a rather unwieldy quantity known as stability-degree. Since then other approaches have been sought to find stable ranges for FI-modules, such as the more symmetric function flavored approach of Hersh and Reiner. In this talk, we will show a different symmetric function approach by using monomial expansions of the corresponding Frobenius series to get stable ranges. In this way, we reprove the stability of the diagonal co-invariants and Kronecker coefficients. We also get new results for stability of Macdonald polynomials and q,t-Kostka numbers.
CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar
Thursday, November 7, 2024 - 3:30pm
Nikita Borisov
Penn
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