Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras

Abstract

Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.

Keywords

• modular lie superalgebra
• graded module
• irreducibility
• highest weight
• 17b10
• 17b50
• 17b70