2018/01/21 by Daniël Kroes, Kroes, Daniël
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1801.06947
openalex publication_date 2018/01/21 · arxiv created 2019/06/24 · arxiv updated 2019/06/25 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Let r and n be positive integers, let Gn be the complex reflection group of n × n monomial matrices whose entries are r^\textrmth roots of unity and let 0 ≤ k ≤ n be an integer. Recently, Haglund, Rhoades and Shimozono (r=1) and Chan and Rhoades (r>1) introduced quotients Rn,k (for r>1) and Sn,k (for r ≥ 1) of the polynomial ring ℂ[x1,…,xn] in n variables, which for k=n reduce to the classical coinvariant algebra attached to Gn. When n=k and r=1, Garsia and Stanton exhibited a quotient of ℂ[yS] isomorphic to the coinvariant algebra, where ℂ[yS] is the polynomial ring in 2n-1 variables whose variables are indexed by nonempty subsets S ⊆ [n]. In this paper, we will define analogous quotients that are isomorphic to Rn,k and Sn,k.