Blocks and characters of $D(2|1;\zeta)$-modules of non-integral weights
Abstract
We classify blocks in the BGG category $\mathcal O$ of modules of non-integral weights for the exceptional Lie superalgebra $D(2|1;\zeta)$. We establish various reduction methods, which connect some types of non-integral blocks of $D(2|1;\zeta)$ with integral blocks of general linear Lie superalgebras $\mathfrak{gl}{(1|1)}$ and $\mathfrak{gl}{(2|1)}$. We compute the characters for irreducible $D(2|1;\zeta)$-modules of non-integral weights in $\mathcal O$.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.02662
- arXiv:
- arXiv:2002.02662
- Bibcode:
- 2020arXiv200202662C
- Keywords:
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- Mathematics - Representation Theory;
- 17B10
- E-Print:
- 27 pages. The reference has been corrected in this version