Canonical bases and Khovanov-Lauda algebras

By M. Varagnolo, E. Vasserot. 2009

49 citations recorded by the source corpus.

We prove some recent conjectures of Khovanov-Lauda concerning the categorification of one-half of the quantum group associated with a simply laced Cartan datum.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8d8ae5fe9eec40b86f7b43a47d9194411b60ddf4

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Citations in the corpus

Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products (2010, methodology): “′ )× D(X0 λ′−λ ) →D(X 0 λ′′−λ ) given by Lusztig’s convolution product ⋆. This category is actually quite closely related to the categories U−and U+ we discussed before. This is essentially proven in [VV], but since it is not stated there in the form most convenient for us, let us state it here: Pro”
Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words (2009, background): “This follows in the simply laced case from Varagnolo and Vasserot [ 23 ] and in general from R. Rouquier (in preparation), who prove that the classes [L] of the graded irreducible R-modules in characteristic zero under the isomorphism γ ∗ from Theorem 4.4 correspond to the dual canonical basis eleme”
Crystals from categorified quantum groups (2009, methodology): “One should be able to deduce a classification of graded simple modules for the algebras R(ν) in the symmetric case using results of [31] and [57] together with Kashiwara and Saito’s geometric construction of crystals [30], but the details of this argument have not appeared.”
Knot Invariants and Higher Representation Theory (2013, methodology): “Conjecturally, the Mazorchuk-Stroppel-Sussan homology is canonically isomorphic to Khovanov-Rozansky homology (see [ MSa ,x7]).”
Representation theory of symmetric groups and related Hecke algebras (2009, methodology): “jective indecomposable modules. This proves for all type Aquivers (ﬁnite or aﬃne) a conjecture of Khovanov and Lauda formulated in [113, §3.4]. Apart from the case e= 2, this result is also proved in [191] by a very diﬀerent method, which works for an arbitrary simply-laced type. The result has also”
Categorifications from planar diagrammatics (2010, background): “respond to multiplication and comultiplication in the quantum group. A direct link between this categoriﬁcation of U+ q and Lusztig’s perverse sheaves construction was found by Varagnolo and Vasserot [47]. Brundan and Kleshchev [7] related these rings to Ariki’s categoriﬁcations of U+ and highest we”