A diagrammatic approach to categorification of quantum groups II

By Mikhail Khovanov, Aaron D. Lauda. 2008

592 citations recorded by the source corpus.

We categorify one-half of the quantum group associated to an arbitrary Cartan datum.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8f92dd52e5e408507c6db9a0c99f49b19a7a785

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Aaron D. Lauda
2. David E. V. Rose
3. Ben Webster
4. Hoel Queffelec
5. Mikhail Khovanov
6. Paul Wedrich
7. Alexander S. Kleshchev
8. Sabin Cautis

In Mathematical Physics

1. David E. V. Rose
2. Aaron D. Lauda
3. Hoel Queffelec
4. Paul Wedrich
5. Ben Webster
6. Mikhail Khovanov
7. Sabin Cautis
8. Alexander S. Kleshchev

Citations in the corpus

• The Odd nilHecke Algebra and its Diagrammatics (2011, background): “The nilHecke algebra plays a central role in the theory of categorified quantum groups, giving rise to an integral categorification of the negative half of Uq(sl2) [10, 7, 15].”
• The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “Our main tool is the higher representation theory of the Khovanov-Lauda categorified quantum group [25, 26, 27] (see also work of Rouquier [48] for an independent construction), in particular, the categorical skew Howe duality of Cautis-Kamnitzer-Licata [8].”
• Categorifications from planar diagrammatics (2010, background): “To get this match, when � has an odd length cycle, the definition of R.�/ should be slightly modified, see the above references and [ 27 ,44].”
• Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words (2009, background): “Khovanov and Lauda [8, 9 ] and Rouquier [21] have introduced a new family of graded algebras whose representation theory is related to categorification of quantum groups.”
• Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “The affine Khovanov-Lauda-Rouquier algebras were introduced independently by Khovanov and Lauda [113, 114] and Rouquier [174].”
• Monoidal categorification of cluster algebras (2014, background): “The Khovanov-Lauda-Rouquier (or simply KLR) algebras, introduced by KhovanovLauda [13, 14] and Rouquier [22] independently, are a family of Z-graded algebras which categorifies the negative half U−q (g) of a symmetrizable quantum group Uq(g).”
• A diagrammatic categorification of the q-Schur algebra (2010, methodology): “Our proof is essentially the same, except that we use the fact that U is an isomorphism and‰n;d is full to avoid having to formulate and use analogues of the results in [14] and [15], which might be hard.”