2019 / December Volume 14 No.4
Odd Singular Vector Formula for General Linear Lie Superalgebras
| Published Date |
2019 / December
|
|---|---|
| Title | Odd Singular Vector Formula for General Linear Lie Superalgebras |
| Author | |
| Keyword | |
| Download | |
| Pagination | 389-402 |
| Abstract | We establish a closed formula for a singular vector of weight $\lambda-\beta$ in the Verma module of highest weight $\lambda$ for
Lie superalgebra ${\mathfrak {gl}}(m|n)$ when $\lambda$ is atypical with respect to an odd positive root $\beta$. It is further shown
that this vector is unique up to a scalar multiple, and it descends to a singular vector, again unique up to a scalar multiple, in
the corresponding Kac module when both $\lambda$ and $\lambda-\beta$ are dominant integral.
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| DOI | |
| AMS Subject Classification |
17B10
|
| Received |
2019-05-09
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| Accepted |
2019-06-25
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