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| Character Formulas for a Class of Simple Restricted Modules over the Simple Lie Superalgebras of Witt Type |
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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 |
| Page view： 801
Net amount： 703 |
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). |
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| 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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