Article

Communications in Mathematical Physics

, Volume 296, Issue 3, pp 827-860

First online:

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

  • Dimitar GrantcharovAffiliated withDepartment of Mathematics, University of Texas at Arlington
  • , Ji Hye JungAffiliated withDepartment of Mathematical Sciences and Research Institute of Mathematics, Seoul National University
  • , Seok-Jin KangAffiliated withDepartment of Mathematical Sciences and Research Institute of Mathematics, Seoul National University
  • , Myungho KimAffiliated withDepartment of Mathematical Sciences and Research Institute of Mathematics, Seoul National University Email author 

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Abstract

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 \({\mathcal {O}_{q}^{\geq 0}}\).