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- W2805543197 abstract "Let $r$ and $n$ be positive integers, let $G_n$ be the complex reflection group of $n times n$ monomial matrices whose entries are $r^{textrm{th}}$ roots of unity and let $0 leq k leq n$ be an integer. Recently, Haglund, Rhoades and Shimozono ($r=1$) and Chan and Rhoades ($r>1$) introduced quotients $R_{n,k}$ (for $r>1$) and $S_{n,k}$ (for $r geq 1$) of the polynomial ring $mathbb{C}[x_1,ldots,x_n]$ in $n$ variables, which for $k=n$ reduce to the classical coinvariant algebra attached to $G_n$. When $n=k$ and $r=1$, Garsia and Stanton exhibited a quotient of $mathbb{C}[mathbf{y}_S]$ isomorphic to the coinvariant algebra, where $mathbb{C}[mathbf{y}_S]$ is the polynomial ring in $2^n-1$ variables whose variables are indexed by nonempty subsets $S subseteq [n]$. In this paper, we will define analogous quotients that are isomorphic to $R_{n,k}$ and $S_{n,k}$." @default.
- W2805543197 created "2018-06-13" @default.
- W2805543197 creator A5031257518 @default.
- W2805543197 date "2018-01-22" @default.
- W2805543197 modified "2023-09-27" @default.
- W2805543197 title "Generalized coinvariant algebras for $G(r,1,n)$ in the Stanley-Reisner setting" @default.
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