JournalsjemsVol. 17, No. 7pp. 1593–1627

Crystal bases for the quantum queer superalgebra

  • Dimitar Grantcharov

    University of Texas at Arlington, USA
  • Ji Hye Jung

    Seoul National University, South Korea
  • Seok-Jin Kang

    Seoul National University, South Korea
  • Masaki Kashiwara

    Kyoto University, Japan
  • Myungho Kim

    Seoul National University, South Korea
Crystal bases for the quantum queer superalgebra cover
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Abstract

In this paper, we develop the crystal basis theory for the quantum queer superalgebra Uq(q(n))U_q(\mathfrak{q}(n)). We define the notion of crystal bases and prove the tensor product rule for Uq(q(n))U_q(\mathfrak{q}(n))-modules in the category Oint0\mathcal{O}^{\ge0}_{\mathrm {int}}. Our main theorem shows that every Uq(q(n))U_q(\mathfrak{q}(n))-module in the category Oint0\mathcal{O}^{\ge0}_{\mathrm {int}} has a unique crystal basis.

Cite this article

Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, Myungho Kim, Crystal bases for the quantum queer superalgebra. J. Eur. Math. Soc. 17 (2015), no. 7, pp. 1593–1627

DOI 10.4171/JEMS/540