Simple character formulas for finite $W$-superalgebras of type $A$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912936959672320 |
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| author | Cheng, Shun-Jen Wang, Weiqiang |
| author_facet | Cheng, Shun-Jen Wang, Weiqiang |
| contents | We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories categorify the tensor product modules of irreducible polynomial representations and their duals over a quantum group of type $A$. Moreover, the standard modules and irreducible modules in these categories categorify the standard basis and Lusztig's dual canonical basis in the tensor product modules. Our formula provides a uniform generalization of several character formulas in BGG categories for Lie superalgebras and for $W$-algebras of type $A$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_01373 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple character formulas for finite $W$-superalgebras of type $A$ Cheng, Shun-Jen Wang, Weiqiang Representation Theory Primary 17B10, 17B37 We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories categorify the tensor product modules of irreducible polynomial representations and their duals over a quantum group of type $A$. Moreover, the standard modules and irreducible modules in these categories categorify the standard basis and Lusztig's dual canonical basis in the tensor product modules. Our formula provides a uniform generalization of several character formulas in BGG categories for Lie superalgebras and for $W$-algebras of type $A$. |
| title | Simple character formulas for finite $W$-superalgebras of type $A$ |
| topic | Representation Theory Primary 17B10, 17B37 |
| url | https://arxiv.org/abs/2603.01373 |