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Transactions of the American Mathematical Society

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A geometric setting for quantum $ \mathfrak{osp}(1\Vert 2)$


Authors: Zhaobing Fan and Yiqiang Li
Journal: Trans. Amer. Math. Soc. 367 (2015), 7895-7916
MSC (2010): Primary 17B37, 14F43
DOI: https://doi.org/10.1090/S0002-9947-2015-06266-7
Published electronically: March 26, 2015
MathSciNet review: 3391903
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Abstract | References | Similar Articles | Additional Information

Abstract: A geometric categorification is given for arbitrary-large-finite-
dimensional quotients of quantum $ \mathfrak{osp}(1\vert 2)$ and tensor products of its simple modules. The modified quantum $ \mathfrak{osp}(1\vert 2)$ of Clark-Wang, a new version in this paper and the modified quantum $ \mathfrak{sl}(2)$ are shown to be isomorphic to each other over a field containing $ \mathbb{Q}(v)$ and $ \sqrt {-1}$.


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Additional Information

Zhaobing Fan
Affiliation: Department of Mathematics, 244 Mathematics Building, University of Buffalo, The State University of New York, Buffalo, New York 14260
Address at time of publication: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: zhaobing@buffalo.edu, fanz@math.ksu.edu

Yiqiang Li
Affiliation: Department of Mathematics, 244 Mathematics Building, University of Buffalo, The State University of New York, Buffalo, New York 14260
Email: yiqiang@buffalo.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06266-7
Keywords: Quantum $\mathfrak{osp}(1\|2)$, quantum modified algebra, tensor product module, categorification, perverse sheaf
Received by editor(s): May 1, 2013
Received by editor(s) in revised form: August 10, 2013, and August 14, 2013
Published electronically: March 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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