Invariants of polynomials mod Frobenius powers

JOURNAL OF ALGEBRA

卷:556

Article

Drescher, C.¹  Shepler, A., V¹ 

[1] Univ North Texas, Dept Math, Denton, TX 76203 USA

关键词: Reflection groups;    Invariant theory;    Catalan numbers;    Fuss-Catalan numbers;    Frobenius map;    (q,t)-binomial coefficients;    Transvections;   

DOI  :  10.1016/j.jalgebra.2020.02.041

来源: Elsevier

【 摘 要 】

Lewis, Reiner, and Stanton conjectured a Hilbert series for a space of invariants under an action of finite general linear groups using (q, t)-binomial coefficients. This work gives an analog in positive characteristic of theorems relating various Catalan numbers to the representation theory of rational Cherednik algebras. They consider a finite general linear group as a reflection group acting on the quotient of a polynomial ring by iterated powers of the irrelevant ideal under the Frobenius map. We prove a variant of their conjecture in the local case, when the group acting fixes a reflecting hyperplane. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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