Canonical bases and KLR-algebras

By M. Varagnolo, E. Vasserot. 2011

210 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/2d289557e84eb1ff7b92663c6bbe7bcac88af0d5

How researchers see this paper

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

In Algebra and Number Theory

1. Jonathan Brundan
2. Mikhail Khovanov
3. Alexander S. Kleshchev
4. Ben Webster
5. Aaron D. Lauda
6. You Qi
7. Seok-Jin Kang
8. Masaki Kashiwara

In Geometry and Topology

1. Ben Webster
2. Jonathan Brundan
3. Alexander S. Kleshchev
4. Mikhail Khovanov
5. Aaron D. Lauda
6. You Qi
7. C. Stroppel
8. Seok-Jin Kang

In Mathematical Physics

1. Jonathan Brundan
2. Alexander S. Kleshchev
3. Ben Webster
4. Mikhail Khovanov
5. You Qi
6. Aaron D. Lauda
7. C. Stroppel
8. Seok-Jin Kang

Citations in the corpus

• Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras (2011, background): “Moreover, when the generalized Cartan matrix is a symmetric matrix, Varagnolo and Vasserot ([17]) and independently Rouquier ( [16]) proved that Kashiwara’s lower global basis or Lusztig’s canonical basis corresponds to”
• An approach to categorification of some small quantum groups II (2012, background): “The direct sum of Grothendieck groups of finitelygenerated projective graded R(ν)-modules, over all ν, can be canonically identified [20, 21, 45] with an integral form of the positive half of the quantum group associated to Γ: U+q,Z(Γ) ∼= ⊕ ν∈NI K0(R(ν)).”
• Finite Dimensional Representations of Khovanov-Lauda-Rouquier algebras I: Finite Type (2012, unknown): “ussion KLR ALGEBRAS 5 in [KL2] shows that the choice of total ordering on I is irrelevant (and indeed, it is included only to match up with the geometric picture in the simply-laced case presented in [VV] and [R2]). At times we will provide references to results in [KL1]. The reader should not be co”
• Simplicity of heads and socles of tensor products (2014, background): “The upper global basis corresponds to the set of isomorphism classes of simple modules over the quiver Hecke algebra or the quantum affine algebras ([2, 15, 16]) under suitable conditions.”
• Monoidal categorification of cluster algebras (2014, background): “Recall that the graded algebra R(β) (β ∈ Q) is geometrically realized as follows ([24]).”
• Homological properties of finite type Khovanov-Lauda-Rouquier algebras (2012, methodology): “lows by the definition in [L1] in simply-laced types or [S] in non-simply-laced types. For simply-laced types over fields of characteristic zero, the results of Rouquier [R2, §5] and Varagnolo-Vasserot [VV] show under the identification from Theorem 2.2 that bλ = [P(λ)], hence also b∗ λ = [L(λ)], for e”
• Mirković–Vilonen polytopes and Khovanov–Lauda–Rouquier algebras (2012, background): “n polytopes and Khovanov-Lauda-Rouquier algebras The KLR polytopes of these representations are independentof q andare given by • • • (2) • • • • (1) (1,1) If one takes the choice of parameters as in [VV11] corresponding to an Ext-algebra ofperversesheavesonthemoduliofrepresentations ofaKronecker qu”
• Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “This prediction was verified, [81], and therefore a connection between representations of cyclotomic Hecke algebras and canonical bases was established.”
• The $p$-Canonical Basis for Hecke Algebras (2015, methodology): “ an algebra. For example, the canonical basis of the quantum group is realized in simply laced type as the classes in the Grothendieck group of indecomposable projective modules for KLR algebras (see [VV11]). Similarly, the Kazhdan-Lusztig basis arises as the classes of indecomposable Soergel bimodu”