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Highest weight modules over Borcherds-Bozec superalgebras and their character formula

Zhaobing Fan, Jiaqi Huang, Seok-Jin Kang, Yong-Su Shin

Abstract

We present and prove the Weyl-Kac type character formula for the irreducible highest weight modules over Borcherds-Bozec superalgebras with dominant integral highest weights.

Highest weight modules over Borcherds-Bozec superalgebras and their character formula

Abstract

We present and prove the Weyl-Kac type character formula for the irreducible highest weight modules over Borcherds-Bozec superalgebras with dominant integral highest weights.
Paper Structure (4 sections, 7 theorems, 88 equations)

This paper contains 4 sections, 7 theorems, 88 equations.

Table of Contents

  1. Odd Borcherds-Cartan Datum
  2. Borcherds-Bozec Superalgebras
  3. Representation Theory and Casimir Operator
  4. The Character Formula

Key Result

Proposition 2.2

Let ${\mathfrak g} = \bigoplus_{\alpha \in \Delta} {\mathfrak g}_{\alpha}$ be a Borcherds-Bozec superalgebra. Then the non-degenerate symmetric bilinear form $( \ \, , \, \ )$ on ${\mathfrak h}$ can be extended to a bilinear form on ${\mathfrak g}$ satisfying the following properties.

Theorems & Definitions (14)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Lemma 2.3
  • proof
  • Proposition 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 4.1
  • ...and 4 more