Coinvariant algebras and fake degrees for spin Weyl groups of exceptional type

TL;DR

This paper computes the spin fake degrees for exceptional Weyl groups, revealing they are palindromic polynomials, and advances understanding of their graded multiplicities in spin coinvariant algebras.

Contribution

It provides the first complete calculation of spin fake degrees for exceptional Weyl groups, highlighting their palindromic nature.

Findings

All spin fake degrees are palindromic polynomials.

Explicit graded multiplicities for simple modules are determined.

Enhances understanding of spin coinvariant algebra structure.

Abstract

We compute all the spin fake degrees for the exceptional Weyl groups, which are by definition the graded multiplicities of the simple modules of a spin Weyl group in its spin coinvariant algebra. The spin fake degrees are all shown to be palindromic polynomials.