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

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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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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan

    Shun-Jen Cheng

  2. Department of Mathematical Sciences, Seoul National University, Seoul, 08826, Korea

    Jae-Hoon Kwon

  3. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

    Weiqiang Wang

Authors
  1. Shun-Jen Cheng
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  2. Jae-Hoon Kwon
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  3. Weiqiang Wang
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Corresponding author

Correspondence to Jae-Hoon Kwon.

Additional information

Communicated by Y. Kawahigashi

Shun-Jen Cheng: Partially supported by a MoST and an Academia Sinica Investigator Grant. Jae-Hoon Kwon: Partially supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1501-01. Weiqiang Wang: Partially supported by an NSF Grant.

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Cheng, SJ., Kwon, JH. & Wang, W. Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C . Commun. Math. Phys. 352, 1091–1119 (2017). https://doi.org/10.1007/s00220-016-2809-2

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