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
paper · pdf · doi:10.48550/arxiv.1801.06947
openalex publication_date 2018/01/21 · 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\ngroup of n \× n monomial matrices whose entries are r^ textrmth\nroots of unity and let 0 \≤ k \≤ n be an integer. Recently, Haglund,\nRhoades and Shimozono (r=1) and Chan and Rhoades (r>1) introduced quotients\nRn,k (for r>1) and Sn,k (for r \≥ 1) of the polynomial ring\n\ℂ[x1,\…,xn] in n variables, which for k=n reduce to the\nclassical coinvariant algebra attached to Gn. When n=k and r=1, Garsia\nand Stanton exhibited a quotient of \ℂ[\yS] isomorphic to\nthe coinvariant algebra, where \ℂ[\yS] is the polynomial\nring in 2n-1 variables whose variables are indexed by nonempty subsets S\n\⊆ [n]. In this paper, we will define analogous quotients that are\nisomorphic to Rn,k and Sn,k.\n