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Irreducible Modules for Super-Virasoro Algebras from Algebraic D-Modules

Haibo Chen, Xiansheng Dai, Dong Liu, Yufeng Pei

Abstract

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on irreducibility preservation and natural isomorphisms. By utilizing these functors, we recover some old irreducible super-Virasoro modules, including those from the irreducible intermediate series as well as irreducible $U(\mathfrak{h})$-free modules. Additionally, we provide several families of new irreducible super-Virasoro modules via our constructed functors.

Irreducible Modules for Super-Virasoro Algebras from Algebraic D-Modules

Abstract

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on irreducibility preservation and natural isomorphisms. By utilizing these functors, we recover some old irreducible super-Virasoro modules, including those from the irreducible intermediate series as well as irreducible -free modules. Additionally, we provide several families of new irreducible super-Virasoro modules via our constructed functors.
Paper Structure (14 sections, 18 theorems, 55 equations)

This paper contains 14 sections, 18 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Constructions of functors
  4. From $\mathcal{D}$-modules to $\mathcal{SD}$-modules
  5. From $\mathcal{SD}$-modules to $\mathfrak{g}[\epsilon]$-modules
  6. Properties of functors $H_{\epsilon,b}$
  7. Preservation of irreducibility
  8. Natural isomorphisms
  9. Applications and examples
  10. Intermediate series modules
  11. $U(\mathfrak{h})$-free modules
  12. Degree two modules
  13. Fraction modules
  14. Special degree $n$ modules

Key Result

Theorem 2.6

Let $M$ be an irreducible $\mathcal{D}$-module.

Theorems & Definitions (37)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4: NS,R
  • Definition 2.5
  • Theorem 2.6: BLZ
  • Definition 2.7: CW
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • ...and 27 more