Character formulae in category $\mathcal O$ for exceptional Lie superalgebras $D(2|1;\zeta)$

Shun-Jen Cheng; Weiqiang Wang

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arXiv · 1704.00846

Character formulae in category $\mathcal O$ for exceptional Lie superalgebras $D(2|1;\zeta)$

Shun-Jen Cheng·Weiqiang Wang

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Abstract

We establish character formulae for representations of the one-parameter family of simple Lie superalgebras $D(2|1;\zeta)$. We provide a complete description of the Verma flag multiplicities of the tilting modules and the projective modules in the BGG category $\mathcal O$ of $D(2|1;\zeta)$-modules of integral weights, for any complex parameter $\zeta$. The composition factors of all Verma modules in $\mathcal O$ are then obtained.

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BibTeX RIS

Shun-Jen Cheng, Weiqiang Wang. 2017-04-04. Character formulae in category $\mathcal O$ for exceptional Lie superalgebras $D(2|1;\zeta)$. https://arxiv.org/abs/1704.00846

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