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A diagrammatic approach to categorification of quantum groups II


Authors: Mikhail Khovanov and Aaron D. Lauda
Journal: Trans. Amer. Math. Soc. 363 (2011), 2685-2700
MSC (2000): Primary 81R50; Secondary 16S99
DOI: https://doi.org/10.1090/S0002-9947-2010-05210-9
Published electronically: November 16, 2010
MathSciNet review: 2763732
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Abstract: We categorify one-half of the quantum group associated to an arbitrary Cartan datum.


References [Enhancements On Off] (What's this?)

  • 1. J. Brundan and A. Kleshchev.
    Hecke-Clifford superalgebras, crystals of type $ A\sb {2l}\sp {(2)}$ and modular branching rules for $ \hat S\sb n$.
    Represent. Theory, 5:317-403 (electronic), 2001, math.RT/0103060. MR 1870595 (2002j:17024)
  • 2. I. Grojnowski and M. Vazirani.
    Strong multiplicity one theorems for affine Hecke algebras of type A.
    Transform. Groups, 6(2):143-155, 2001. MR 1835669 (2002c:20008)
  • 3. L. Kauffman and S. Lins.
    Temperley-Lieb recoupling theory and invariants of $ 3$-manifolds, volume 134 of Annals of Mathematics Studies.
    Princeton University Press, 1994. MR 1280463 (95c:57027)
  • 4. M. Khovanov and A. Lauda.
    A diagrammatic approach to categorification of quantum groups I. Represenation Theory, 13:309-347 (electronic), 2009. MR 2525917 (2010i:17023)
  • 5. A. Kleshchev.
    Linear and projective representations of symmetric groups, volume 163 of Cambridge Tracts in Mathematics.
    Cambridge Univ. Press, 2005. MR 2165457 (2007b:20022)
  • 6. G. Lusztig.
    Introduction to quantum groups, volume 110 of Progress in Mathematics.
    Birkhäuser Boston Inc., Boston, MA, 1993. MR 1227098 (94m:17016)
  • 7. M. Okado and H. Yamane.
    $ R$-matrices with gauge parameters and multi-parameter quantized enveloping algebras.
    In Special functions (Okayama, 1990), ICM-90 Satell. Conf. Proc., pages 289-293. Springer, Tokyo, 1991. MR 1166822 (93f:17025)
  • 8. N. Reshetikhin.
    Multiparameter quantum groups and twisted quasitriangular Hopf algebras.
    Lett. Math. Phys., 20(4):331-335, 1990. MR 1077966 (91k:17012)
  • 9. M. Vazirani.
    Irreducible modules over the affine Hecke algebra: A strong multiplicity one result.
    Ph.D. thesis, UC Berkeley, 1999, math.RT/0107052.

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Additional Information

Mikhail Khovanov
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: khovanov@math.columbia.edu

Aaron D. Lauda
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: lauda@math.columbia.edu

DOI: https://doi.org/10.1090/S0002-9947-2010-05210-9
Keywords: Categorification, quantum groups, Grothendieck ring, canonical basis
Received by editor(s): June 6, 2009
Received by editor(s) in revised form: September 9, 2009
Published electronically: November 16, 2010
Additional Notes: The first author was fully supported by the IAS and the NSF grants DMS–0635607 and DMS-0706924 while working on this paper
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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