Algebras and Representation Theory

, Volume 20, Issue 2, pp 469–486 | Cite as

A Categorification of \(\displaystyle {\mathfrak q} (2)\)-Crystals

  • Dimitar Grantcharov
  • Ji Hye Jung
  • Seok-Jin Kang
  • Myungho Kim


We provide a categorification of \(\mathfrak {q}(2)\)-crystals on the singular \(\mathfrak {gl}_{n}\)-category \({\mathcal O}_{n}\). Our result extends the \(\mathfrak {gl}_{2}\)-crystal structure on \(\text {Irr} ({\mathcal O}_{n})\) induced from the work of Bernstein-Frenkel-Khovanov. Further properties of the \({\mathfrak q}(2)\)-crystal \(\text {Irr} ({\mathcal O}_{n})\) are also discussed.


Crystal bases Odd Kashiwara operators Quantum queer superalgebras \(\displaystyle {\mathfrak q} (2)\)-categorification 

Mathematics Subject Classification (2010)

17B37 81R50 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Dimitar Grantcharov
    • 1
  • Ji Hye Jung
    • 2
  • Seok-Jin Kang
    • 3
  • Myungho Kim
    • 4
  1. 1.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA
  2. 2.Department of Mathematical SciencesSeoul National UniversitySeoulKorea
  3. 3.Department of Mathematical Sciences and Research Institute of MathematicsSeoul National UniversitySeoulKorea
  4. 4.Department of MathematicsKyung Hee UniversitySeoulKorea

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