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Communications in Mathematical Physics

, Volume 352, Issue 3, pp 1091–1119 | Cite as

Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C

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

Abstract

For the BGG category of \({{\mathfrak{q}}(n)}\)-modules of half-integer weights, a Kazhdan–Lusztig conjecture à la Brundan is formulated in terms of categorical canonical basis of the nth tensor power of the natural representation of the quantum group of type C. For the BGG category of \({{\mathfrak{q}}(n)}\)-modules of congruent non-integral weights, a Kazhdan–Lusztig conjecture is formulated in terms of canonical basis of a mixed tensor of the natural representation and its dual of the quantum group of type A. We also establish a character formula for the finite-dimensional irreducible \({\mathfrak{q}(n)}\)-modules of half-integer weights in terms of type C canonical basis of the corresponding q-wedge space.

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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
  3. 3.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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