Geodesic
Ordered Set Partitions and the 0-Hecke Algebra
Séminaire lotharingien de combinatoire, 80B (2018)

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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. 

@article{SLC_2018_80B_a8,
     author = {Jia Huang and Brendon Rhoades},
     title = {Ordered {Set} {Partitions} and the {0-Hecke} {Algebra}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a8/}
}
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TI  - Ordered Set Partitions and the 0-Hecke Algebra
JO  - Séminaire lotharingien de combinatoire
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VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a8/
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Jia Huang; Brendon Rhoades. Ordered Set Partitions and the 0-Hecke Algebra. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a8/