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Communications in Mathematical Physics

, Volume 346, Issue 3, pp 945–965 | Cite as

Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras

  • Shun-Jen Cheng
  • Jae-Hoon KwonEmail author
Article

Abstract

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra \({\mathfrak{q}(n)}\). It is given in terms of the Brundan’s work on finite-dimensional integer weight \({\mathfrak{q}(n)}\)-modules by means of Lusztig’s canonical basis. Using this viewpoint we compute the characters of the finite-dimensional half-integer weight irreducible modules. For a large class of irreducible modules whose highest weights are of special types (i.e., totally connected or totally disconnected) we derive closed-form character formulas that are reminiscent of the Kac–Wakimoto character formula for basic Lie superalgebras.

Keywords

Character Formula Parabolic Subalgebras Levi Subalgebra Dual Canonical Basis Canonical Basis Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Mathematics, Academia SinicaTaipeiTaiwan
  2. 2.Department of Mathematical SciencesSeoul National UniversitySeoulKorea

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