Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups

Abstract

For finite complex reflexion groups, we consider the graded $W$-modules of diagonally harmonic polynomials in $r$ sets of variables, and show that associated Hilbert series may be described in a global manner, independent of the value of $r$.

12 pages, Removed a (wrong) conjecture, and reformulated in agreement. Also cleared up section on low degree terms

References in corpus (3)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• On the quotient ring by diagonal harmonics
• Higher Trivariate Diagonal Harmonics via generalized Tamari Posets

Cited by in corpus (8)

• Higher Trivariate Diagonal Harmonics via generalized Tamari Posets
• Combinatorics of r-Dyck paths, r-Parking functions, and the r-Tamari lattices
• FI_W-modules and stability criteria for representations of the classical Weyl groups
• The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture
• Interlaced rectangular parking functions
• $(G{L}_k\times S_n)$-Modules of Multivariate Diagonal Harmonics
• New Formulas and Conjectures for the Nabla Operator
• A Survey of $q$-Whittaker polynomials