Non-restricted representations of contact and special contact Lie superalgebras of odd type

TL;DR

This paper investigates non-restricted representations of contact and special contact Lie superalgebras of odd type over fields of characteristic p>3, characterizing simple modules via induced Kac modules and p-characters.

Contribution

It provides a comprehensive classification of simple modules with various types of p-characters for these superalgebras, using induced Kac modules.

Findings

Characterization of simple modules with nonsingular or Δ-invertible p-characters

Classification of simple modules with regular semisimple p-characters

Use of induced Kac modules to analyze representations

Abstract

Let $\frak{g}$ be a contact Lie superalgebra of odd type or special contact Lie superalgebra of odd type over an algebraically closed field of characteristic $p>3$. In this paper we study non-restricted representations of $\frak{g}$. By using induced Kac modules, we characterize all simple $\frak{g}$-modules with nonsingular or $\Delta$-invertible $p$-characters. We also obtain all simple $\frak{g}$-modules with regular semisimple $p$-characters.