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


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.


Character Formula Parabolic Subalgebras Levi Subalgebra Dual Canonical Basis Canonical Basis Element 
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© 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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