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Generalized coinvariant algebras for in the Stanley-Reisner setting
Let and be positive integers, let be the complex reflection
group of monomial matrices whose entries are
roots of unity and let be an integer. Recently, Haglund,
Rhoades and Shimozono () and Chan and Rhoades () introduced quotients
(for ) and (for ) of the polynomial ring
in variables, which for reduce to the
classical coinvariant algebra attached to . When and , Garsia
and Stanton exhibited a quotient of isomorphic to
the coinvariant algebra, where is the polynomial
ring in variables whose variables are indexed by nonempty subsets . In this paper, we will define analogous quotients that are
isomorphic to and