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- W3026467609 abstract "Abstract Let r be a positive integer and let G n be the reflection group of n × n monomial matrices whose entries are rth complex roots of unity and let k ≤ n . We define and study two new graded quotients R n , k and S n , k of the polynomial ring C [ x 1 , … , x n ] in n variables. When k = n , both of these quotients coincide with the classical coinvariant algebra attached to G n . The algebraic properties of our quotients are governed by the combinatorial properties of k-dimensional faces in the Coxeter complex attached to G n (in the case of R n , k ) and r-colored ordered set partitions of { 1 , 2 , … , n } with k blocks (in the case of S n , k ). Our work generalizes a construction of Haglund, Rhoades, and Shimozono from the symmetric group S n to the more general wreath products G n ." @default.
- W3026467609 created "2020-05-29" @default.
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- W3026467609 date "2020-09-01" @default.
- W3026467609 modified "2023-09-24" @default.
- W3026467609 title "Generalized coinvariant algebras for wreath products" @default.
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- W3026467609 doi "https://doi.org/10.1016/j.aam.2020.102060" @default.
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