Parabolic-equivariant modules over polynomial rings in infinitely many variables

2024/07/02 by Teresa Yu, Yu, Teresa · 2 citations
Mathematics · Computer Science · #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2407.02588

Abstract

We study the category of P-equivariant modules over the infinite variable polynomial ring, where P denotes the subgroup of the infinite general linear group GL(C^∞) consisting of elements fixing a flag in C^∞ with each graded piece infinite-dimensional. We decompose the category into simpler pieces that can be described combinatorially, and prove a number of finiteness results, such as finite generation of local cohomology and rationality of Hilbert series. Furthermore, we show that this category is equivalent to the category of representations of a particular combinatorial category generalizing FI.

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