DOAJ Open Access 2011

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

J. Haglund

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Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (1)

J. Haglund

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APA MLA BibTeX

Haglund, J. (2011). A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version). https://doi.org/10.46298/dmtcs.2924

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2924

Informasi Jurnal

Tahun Terbit: 2011
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2924
Akses: Open Access ✓