The CAGE (Combinatorics, Algebra, and Geometry) Seminar: Nikita Borisov, 7 November 2024


Representation stability and stable ranges via monomial expansions

Nikita Borisov | 2024-11-07 at 3:30 PM, at David Rittenhouse Laboratory (UPenn), room 2C4

Abstract: 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.


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