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Fake degrees of classical Weyl groups

William M. McGovern

Abstract

We compute the fake degrees of representations of classical Weyl groups in terms of domino tableaux.

Fake degrees of classical Weyl groups

Abstract

We compute the fake degrees of representations of classical Weyl groups in terms of domino tableaux.
Paper Structure (3 sections, 5 theorems, 15 equations)

This paper contains 3 sections, 5 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. Types $B$ and $C$
  3. Type $D$

Key Result

Theorem 1

The fake degree $f_\lambda$ corresponding to $\lambda$ is given by where for a partition $\alpha=(\alpha_1,\alpha_2,\ldots)$ of $r$ and $f_\lambda$ denotes the fake degree of the representation $V_\lambda$ corresponding to $\lambda$. Equivalently, the multiplicity of $V_\lambda$ in the $k$-th graded piece of the coinvariant algebra $C$ is the number of standard tableaux

Theorems & Definitions (7)

  • Theorem 1
  • Theorem 2
  • proof
  • Corollary 1
  • proof
  • Theorem 3
  • Theorem 4