Highest Weight Modules Over Quantum Queer Superalgebra {U_q(mathfrak {q}(n))} |
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| Authors: | Dimitar Grantcharov Ji Hye Jung Seok-Jin Kang Myungho Kim |
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| Affiliation: | 1. Department of Mathematics, University of Texas at Arlington, Arlington, TX, 76021, USA
2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, San 56-1 Sillim-dong, Gwanak-gu, Seoul, 151-747, Korea
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| Abstract: | In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra Uq(mathfrak q(n)){U_q(mathfrak {q}(n))}. The key ingredients are the triangular decomposition of Uq(mathfrak q(n)){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 Uq(mathfrak q(n)){U_q(mathfrak {q}(n))}-modules in the category Oq 3 0{mathcal {O}_{q}^{geq 0}}. |
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