Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Conference papers

A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version)

Abstract : A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series.
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-01215103
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, October 13, 2015 - 3:06:50 PM
Last modification on : Friday, June 28, 2019 - 2:48:03 PM
Long-term archiving on: : Thursday, April 27, 2017 - 12:21:58 AM

File

dmAO0140.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

J. Haglund. A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version). 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.445-456, ⟨10.46298/dmtcs.2924⟩. ⟨hal-01215103⟩

Share

Metrics

Record views

52

Files downloads

417