Representations of shifted super Yangians and finite $W$-superalgebras of type A
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908885001961472 |
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| author | Lu, Kang Peng, Yung-Ning |
| author_facet | Lu, Kang Peng, Yung-Ning |
| contents | In this article, we study the representation theory of shifted super Yangians and finite $W$-superalgebras of type A. A criterion for the finite dimensionality of irreducible modules is obtained in the standard parity case. Furthermore, we provide an explicit Gelfand-Tsetlin character formula for Verma modules of finite $W$-superalgebras. As an application, we show that the centers of the finite $W$-superalgebras associated to any even nilpotent elements belonging to the same general linear Lie superalgebra are all isomorphic to the center of the universal enveloping superalgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07541 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representations of shifted super Yangians and finite $W$-superalgebras of type A Lu, Kang Peng, Yung-Ning Representation Theory Quantum Algebra In this article, we study the representation theory of shifted super Yangians and finite $W$-superalgebras of type A. A criterion for the finite dimensionality of irreducible modules is obtained in the standard parity case. Furthermore, we provide an explicit Gelfand-Tsetlin character formula for Verma modules of finite $W$-superalgebras. As an application, we show that the centers of the finite $W$-superalgebras associated to any even nilpotent elements belonging to the same general linear Lie superalgebra are all isomorphic to the center of the universal enveloping superalgebra. |
| title | Representations of shifted super Yangians and finite $W$-superalgebras of type A |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2603.07541 |