Communications in Mathematical Physics

, Volume 296, Issue 3, pp 827–860

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

  • Dimitar Grantcharov
  • Ji Hye Jung
  • Seok-Jin Kang
  • Myungho Kim
Article

DOI: 10.1007/s00220-009-0962-6

Cite this article as:
Grantcharov, D., Jung, J.H., Kang, S. et al. Commun. Math. Phys. (2010) 296: 827. doi:10.1007/s00220-009-0962-6

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

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Dimitar Grantcharov
    • 1
  • Ji Hye Jung
    • 2
  • Seok-Jin Kang
    • 2
  • Myungho Kim
    • 2
  1. 1.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA
  2. 2.Department of Mathematical Sciences and Research Institute of MathematicsSeoul National UniversitySeoulKorea