Character Formulas for a Class of Simple Restricted Modules over the Simple Lie Superalgebras of Witt Type

Citation:

Yu-Feng YAO.Character Formulas for a Class of Simple Restricted Modules over the Simple Lie Superalgebras of Witt Type[J].Chinese Annals of Mathematics B,2020,41(1):49~60
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Authors:

Yu-Feng YAO;

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11771279, 11671138) and the Natural Science Foundation of Shanghai (No.16ZR1415000).
Abstract: Let $F$ be an algebraically closed field of prime characteristic, and $W(m,n,\textbf{1})$ be the simple restricted Lie superalgebra of Witt type over $F$, which is the Lie superalgebra of superderivations of the superalgebra $\fraka(m;\textbf{1})\otimes \wedge(n)$, where $\fraka(m;\textbf{1})$ is the truncated polynomial algebra with $m$ indeterminants and $\wedge(n)$ is the Grassmann algebra with $n$ indeterminants. In this paper, the author determines the character formulas for a class of simple restricted modules of $W(m,n,\textbf{1})$ with atypical weights of type I.

Keywords:

Restricted Lie superalgebra, Witt type Lie superalgebra, Restricted& representation, Typical (atypical) weight, Character formula

Classification:

17B10, 17B50
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