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Unitary modules over the gap-$p$ Virasoro algebras

Chengkang Xu

Abstract

For any irreducible Harish-Chandra module $V$ over the gap-$p$ Virasoro algebra, we determine the condition for $V$ to be unitary.

Unitary modules over the gap-$p$ Virasoro algebras

Abstract

For any irreducible Harish-Chandra module over the gap- Virasoro algebra, we determine the condition for to be unitary.
Paper Structure (5 sections, 17 theorems, 52 equations)

This paper contains 5 sections, 17 theorems, 52 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Highest weight modules
  4. Conjugate-linear anti-involutions of $\mathfrak{g}$
  5. Unitary Harish-Chandra modules

Key Result

Proposition 2.4

The Verma module $M_{\mathcal{V},\phi}$ over $\mathcal{V}$ is irreducible if and only if $\Phi_{h,c}(\alpha,\beta)=0$ for some $\alpha,\beta\in\mathbb{Z}_+$, where $h=\phi(L_0), c=\phi(C_0)$ and

Theorems & Definitions (30)

  • Definition 2.1
  • Remark 2.2
  • Definition 2.3
  • Proposition 2.4
  • Proposition 2.5
  • Definition 2.6
  • Proposition 2.7
  • Proposition 2.8
  • Proposition 2.9
  • Proposition 3.1
  • ...and 20 more