A diagrammatic approach to categorification of quantum groups. II. (English) Zbl 1214.81113

Summary: [For part I see the authors, Represent. Theory 13, 309–347 (2009; Zbl 1194.81117).]
We categorify one-half of the quantum group associated to an arbitrary Cartan datum.


17B37 Quantum groups (quantized enveloping algebras) and related deformations
16T20 Ring-theoretic aspects of quantum groups


Zbl 1194.81117
Full Text: DOI arXiv


[1] Jonathan Brundan and Alexander Kleshchev, Hecke-Clifford superalgebras, crystals of type \?_{2\?}\?²\? and modular branching rules for \?_{\?}, Represent. Theory 5 (2001), 317 – 403. · Zbl 1005.17010
[2] I. Grojnowski and M. Vazirani, Strong multiplicity one theorems for affine Hecke algebras of type A, Transform. Groups 6 (2001), no. 2, 143 – 155. · Zbl 1056.20002
[3] 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. · Zbl 0821.57003
[4] Mikhail Khovanov and Aaron D. Lauda, A diagrammatic approach to categorification of quantum groups. I, Represent. Theory 13 (2009), 309 – 347. · Zbl 1188.81117
[5] Alexander Kleshchev, Linear and projective representations of symmetric groups, Cambridge Tracts in Mathematics, vol. 163, Cambridge University Press, Cambridge, 2005. · Zbl 1080.20011
[6] George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. · Zbl 0788.17010
[7] Masato Okado and Hiroyuki Yamane, \?-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. · Zbl 0774.17022
[8] N. Reshetikhin, Multiparameter quantum groups and twisted quasitriangular Hopf algebras, Lett. Math. Phys. 20 (1990), no. 4, 331 – 335. · Zbl 0719.17006
[9] M. Vazirani. Irreducible modules over the affine Hecke algebra: A strong multiplicity one result. Ph.D. thesis, UC Berkeley, 1999, math.RT/0107052.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.