A diagrammatic approach to categorification of quantum groups II
HTML articles powered by AMS MathViewer
- by Mikhail Khovanov and Aaron D. Lauda PDF
- Trans. Amer. Math. Soc. 363 (2011), 2685-2700 Request permission
Abstract:
We categorify one-half of the quantum group associated to an arbitrary Cartan datum.References
- Jonathan Brundan and Alexander Kleshchev, Hecke-Clifford superalgebras, crystals of type $A_{2l}^{(2)}$ and modular branching rules for $\hat S_n$, Represent. Theory 5 (2001), 317–403. MR 1870595, DOI 10.1090/S1088-4165-01-00123-6
- I. Grojnowski and M. Vazirani, Strong multiplicity one theorems for affine Hecke algebras of type A, Transform. Groups 6 (2001), no. 2, 143–155. MR 1835669, DOI 10.1007/BF01597133
- Louis H. Kauffman and Sóstenes L. Lins, Temperley-Lieb recoupling theory and invariants of $3$-manifolds, Annals of Mathematics Studies, vol. 134, Princeton University Press, Princeton, NJ, 1994. MR 1280463, DOI 10.1515/9781400882533
- Mikhail Khovanov and Aaron D. Lauda, A diagrammatic approach to categorification of quantum groups. I, Represent. Theory 13 (2009), 309–347. MR 2525917, DOI 10.1090/S1088-4165-09-00346-X
- Alexander Kleshchev, Linear and projective representations of symmetric groups, Cambridge Tracts in Mathematics, vol. 163, Cambridge University Press, Cambridge, 2005. MR 2165457, DOI 10.1017/CBO9780511542800
- George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1227098
- Masato Okado and Hiroyuki Yamane, $R$-matrices with gauge parameters and multi-parameter quantized enveloping algebras, Special functions (Okayama, 1990) ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, pp. 289–293. MR 1166822
- N. Reshetikhin, Multiparameter quantum groups and twisted quasitriangular Hopf algebras, Lett. Math. Phys. 20 (1990), no. 4, 331–335. MR 1077966, DOI 10.1007/BF00626530
- M. Vazirani. Irreducible modules over the affine Hecke algebra: A strong multiplicity one result. Ph.D. thesis, UC Berkeley, 1999, math.RT/0107052.
Additional Information
- Mikhail Khovanov
- Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
- MR Author ID: 363306
- Email: khovanov@math.columbia.edu
- Aaron D. Lauda
- Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
- ORCID: setImmediate$0.06573403963950497$1
- Email: lauda@math.columbia.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2763732