Séminaire Lotharingien de Combinatoire, 80B.9 (2018), 12 pp.
Jia Huang and Brendon Rhoades
Ordered Set Partitions and the 0-Hecke Algebra
Abstract.
Haglund, Rhoades, and Shimozono recently introduced a quotient
Rn,k of the polynomial
ring Q[x1, ..., xn] depending on
two positive integers k <= n, which reduces to the classical
coinvariant algebra of the symmetric group Sn if k = n.
They determined the graded Sn-module structure of
Rn,k and
related it to the Delta Conjecture in the theory of Macdonald
polynomials.
We introduce an analogous quotient Sn,k and determine its
structure as a graded module over the (type A) 0-Hecke algebra
Hn(0), a deformation of the group algebra of Sn.
When k = n we recover earlier results of the first author regarding
the I>Hn(0)-action on the coinvariant algebra.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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