On the quotient ring by diagonal harmonics

Details On the quotient ring by diagonal harmonics On the quotient ring by diagonal harmonics

2002-08-16

arxiv.org/abs/math/0208126v2

Mathematics

Representation Theory

Scientific paper

10.1007/s00222-003-0296-5

For a Weyl group W and its reflection representation mathfrak{h}, we find the
character and Hilbert series for a quotient ring of C[mathfrak{h} oplus
mathfrak{h}^*] by an ideal containing the W--invariant polynomials without
constant term. This confirms conjectures of Haiman. The proof makes use of
rational Cherednik algebras, as studied by Etingof and Ginzburg, and others.

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