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Highest Weight Modules Over Quantum Queer Superalgebra \({U_q(\mathfrak {q}(n))}\)

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In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra \({U_q(\mathfrak {q}(n))}\). The key ingredients are the triangular decomposition of \({U_q(\mathfrak {q}(n))}\) and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for \({U_q(\mathfrak {q}(n))}\)-modules in the category \({\mathcal {O}_{q}^{\geq 0}}\).

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Arlington, Arlington, TX, 76021, USA

    Dimitar Grantcharov

  2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, San 56-1 Sillim-dong, Gwanak-gu, Seoul, 151-747, Korea

    Ji Hye Jung, Seok-Jin Kang & Myungho Kim

Authors
  1. Dimitar Grantcharov
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  2. Ji Hye Jung
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  3. Seok-Jin Kang
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  4. Myungho Kim
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Corresponding author

Correspondence to Myungho Kim.

Additional information

Communicated by Y. Kawahigashi

This research was supported by a UT Arlington REP Grant.

This research was supported by KRF Grant # 2007-341-C00001.

This research was supported by BK21 Mathematical Sciences Division.

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Grantcharov, D., Jung, J.H., Kang, SJ. et al. Highest Weight Modules Over Quantum Queer Superalgebra \({U_q(\mathfrak {q}(n))}\) . Commun. Math. Phys. 296, 827–860 (2010). https://doi.org/10.1007/s00220-009-0962-6

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