2-Kac-Moody algebras

Abstract

We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type A. We relate categorifications relying on K_0 properties and 2-representations.

References in corpus (2)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• A categorification of quantum sl(2)

Cited by in corpus (231)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras
• Crystals from categorified quantum groups
• Quantum Grothendieck rings and derived Hall algebras
• Diagrammatics for Soergel categories
• Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products
• Triangular bases in quantum cluster algebras and monoidal categorification conjectures
• Quiver Schur algebras and q-Fock space
• Heisenberg categorification and Hilbert schemes
• Canonical bases and higher representation theory
• Affine highest weight categories and affine quasihereditary algebras
• Etingof conjecture for quantized quiver varieties
• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• The odd nilHecke algebra and its diagrammatics
• On uniqueness of tensor products of irreducible categorifications
• Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebras
• Canonical bases and Khovanov-Lauda algebras
• A Prehistory of n-Categorical Physics
• Deformations of colored sl(N) link homologies via foams
• Higher-Dimensional Algebra VII: Groupoidification
• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• An introduction to diagrammatic algebra and categorified quantum sl(2)
• Monoidal categorification and quantum affine algebras
• Hecke algebras, finite general linear groups, and Heisenberg categorification
• On the center of quiver-Hecke algebras
• Formal Hecke algebras and algebraic oriented cohomology theories
• Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties
• An approach to categorification of some small quantum groups II
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Quiver Hecke superalgebras
• Categorifying fractional Euler characteristics, Jones-Wenzl projector and $3j$-symbols
• Categorifications from planar diagrammatics
• An odd categorification of quantum sl(2)
• Current algebras and categorified quantum groups
• Vertex operators and 2-representations of quantum affine algebras
• Modular representation theory in type A via Soergel bimodules
• Koszul duality between Higgs and Coulomb categories $\mathcal{O}$
• Supports of simple modules in cyclotomic Cherednik categories O
• Highest weight categories arising from Khovanov's diagram algebra III: category O
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Monoidal categorification of cluster algebras II
• Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O
• Graded $q$-Schur algebras
• Categorification of quantum Kac-Moody superalgebras
• Supercategorification of quantum Kac-Moody algebras II
• Representations of the oriented skein category
• Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A
• Lectures on canonical and crystal bases of Hall algebras
• A comparison of Newton-Okounkov polytopes of Schubert varieties
• A categorical action on quantized quiver varieties
• A categorification of quantum sl(2) at prime roots of unity
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality
• The many graded cellular bases of Hecke algebras
• Clasp technology to knot homology via the affine Grassmannian
• Rigidity in higher representation theory
• Canonical basis, KLR-algebras and parity sheaves
• sl(N)-Web categories
• Annular Evaluation and Link Homology
• Cyclicity for categorified quantum groups
• A diagrammatic categorification of the q-Schur algebra
• Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra
• An approach to categorification of Verma modules
• Generalised column removal for graded homomorphisms between Specht modules
• Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types
• Highest weight sl_2-categorifications I: crystals
• Braid group actions via categorified Heisenberg complexes
• Simple transitive $2$-representations and Drinfeld center for some finitary $2$-categories
• Quantum gl(1|1) and tangle Floer homology
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Cyclotomic Yokonuma-Hecke algebras are cyclotomic quiver Hecke algebras
• Simple transitive 2-representations for two non-fiat 2-categories of projective functors
• Super Kac-Moody 2-categories
• A categorification of U_q sl(1,1) as an algebra
• The differential graded odd nilHecke algebra
• Transitive 2-representations of finitary 2-categories
• Duflo involutions for 2-categories associated to tree quivers
• Specht modules for quiver Hecke algebras of type $C$
• Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of Type A
• Categorification at prime roots of unity and hopfological finiteness
• Quantum Shuffles and Quantum Supergroups of Basic Type
• Quiver Schur algebras and Koszul duality
• Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)
• Categorification of tensor powers of the vector representation of $U_q(\mathfrak{gl}(1|1))$
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• Categorical actions on unipotent representations I. Finite unitary groups
• Seminormal forms and cyclotomic quiver Hecke algebras of type $A$
• The sl(N)-web algebras and dual canonical bases
• Advances in R-matrices and their applications (after Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,...)
• Unfurling Khovanov-Lauda-Rouquier algebras
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Isotypic faithful $2$-representations of $\mathcal{J}$-simple fiat $2$-categories
• Generic ${\mathfrak{gl}}_2$-foams, web and arc algebras
• Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
• The Categorified Heisenberg Algebra I: A Combinatorial Representation
• Centers of KLR algebras and cohomology rings of quiver varieties
• On the structure of cyclotomic nilHecke algebras
• Characterisation and applications of $\mathbb{k}$-split bimodules
• On the definition of Kac-Moody 2-category
• The Feigin Tetrahedron
• Quiver Hecke algebras and 2-Lie algebras
• p-DG cyclotomic nilHecke algebras
• Highest weight sl_2-categorifications II: structure theory
• Categorical representations and KLR algebras
• Representations of Khovanov-Lauda-Rouquier algebras III: Symmetric Affine Type
• DG structures on odd categorified quantum sl(2)
• The affine VW supercategory
• Ozsvath-Szabo bordered algebras and subquotients of category O
• Morita equivalences for cyclotomic Hecke algebras of type B and D
• Categorification of highest weight modules over quantum generalized Kac-Moody algebras
• Categorification of tensor product representations of sl(k) and category O
• Biadjointness in cyclic Khovanov-Lauda-Rouquier Algebras
• Laurent phenomenon and simple modules of quiver Hecke algebras
• Towards multiplicities for categories O of cyclotomic rational Cherednik algebras
• Representation type of finite quiver Hecke algebras of type $A_{2\ell }^{(2)}$
• Affinizations and R-matrices for quiver Hecke algebras
• Twisted Coxeter elements and folded AR-quivers via Dynkin diagram automorphisms: I
• Folding KLR algebras
• On the monoidality of Saito reflection functors
• Graded induction for Specht modules
• Cuspidal systems for affine Khovanov-Lauda-Rouquier algebras
• Representations of Quiver Hecke Algebras via Lyndon Bases
• Generalized trace and modified dimension functions on ribbon categories
• Polynomial representations and categorifications of Fock Space
• Homogeneous representations of Type A KLR-algebras and Dyck paths
• Localizations for quiver Hecke algebras
• Odd Khovanov homology for tangles
• An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras
• Homomorphisms between standard modules over finite type KLR algebras
• The Khovanov-Lauda 2-category and categorifications of a level two quantum sl(n) representation
• Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types
• Quiver Schur algebras and cohomological Hall algebras
• Additive versus abelian 2-representations of fiat 2-categories
• On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution
• Polynomial functors and categorifications of Fock space
• Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup
• Affine Hecke algebras and generalisations of quiver Hecke algebras for type B
• On geometric realizations of quantum modified algebras and their canonical bases, II
• Categorical representations, KLR algebras and Koszul duality
• Representations of orientifold Khovanov-Lauda-Rouquier algebras and the Enomoto-Kashiwara algebra
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Planar diagrammatics of self-adjoint functors and recognizable tree series
• Affine quiver Schur algebras and $p$-adic $G{L}_n$
• Universal Verma modules and the Misra-Miwa Fock space
• Type C blocks of super category O
• Crystal bases and categorifications
• A categorification of the positive half of quantum gl(m|1)
• Graded cellular basis and Jucys-Murphy elements for generalized blob algebras
• Monoidal categories associated with strata of flag manifolds
• Representations of general linear groups and categorical actions of Kac-Moody algebras
• The idempotents in cyclotomic Hecke algebras and periodic property of the Jucys-Murphy elements
• KLR and Schur algebras for curves and semi-cuspidal representations
• Trivalent vertices and bordered knot Floer homology in the standard basis
• Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words
• Representation type of finite quiver Hecke algebras of type $A_{\ell }^{(1)}$ for arbitrary parameters
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Coidempotent subcoalgebras and short exact sequences of finitary 2-representations
• Specht modules labelled by hook bipartitions I
• Pyramids and 2-representations
• Presentations for Generalized nilHecke Algebras
• Notes on parameters of quiver Hecke algebras
• Whittaker coinvariants for $\mathrm{GL}(m|n)$
• Monoidal categorification of cluster algebras (merged version)
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach
• An equivalence between truncations of categorified quantum groups and Heisenberg categories
• Modular Representation Theory of Symmetric Groups
• Categorification of the ring of cyclotomic integers for products of two primes
• Geometric realizations of Lusztig's symmetries
• Semi-invariants of filtered quiver representations with at most two pathways
• On 2-Verma modules for quantum ${\mathfrak{sl}}_2$
• Associated graded of Hodge modules and categorical sl_2 actions
• Crystal of affine ${\widehat{\mathfrak{sl}}}_{\ell }$ and Hecke algebras at a primitive $2\ell$th root of unity
• A Demazure Character Formula for the Product Monomial Crystal
• The nil-blob algebra: An incarnation of type ${\tilde{A}}_1$ Soergel calculus and of the truncated blob algebra
• Rational Ringel-Hall algebras, Hall polynomials of affine type and Canonical bases
• Canonical bases for the quantum extended Kac-Moody algebras and Hall polynomials
• Path combinatorics and light leaves for quiver Hecke algebras
• Categorification of the Catalan monoid
• A categorical action of the shifted $q=0$ affine algebra
• Categorical actions and multiplicities in the Deligne category $\underline{Rep}(G{L}_t)$
• A categorical equivalence between affine Yokonuma-Hecke algebras and some quiver Hecke algebras
• Derived equivalences and sl_2-categorifications for U_q(gl_n)
• Affine Hecke algebras of type D and generalisations of quiver Hecke algebras
• Clifford-symmetric polynomials
• On selfadjoint functors satisfying polynomial relations
• Cyclotomic Carter-Payne homomorphisms
• Combinatorial Auslander-Reiten quivers and reduced expressions
• A categorification of $\mathfrak{q}(2)$-crystals
• Higher Representation Theory and Quantum Affine Schur-Weyl Duality
• Dual canonical bases for unipotent groups and base affine spaces
• Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A
• Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula
• Knizhnik--Zamolodchikov functor for degenerate double affine Hecke algebras : algebraic theory
• Sub-bimodules of the identity bimodule for cyclic quivers
• Categorical crystals for quantum affine algebras
• Categorification of Lie algebras [d'apres Rouquier, Khovanov-Lauda]
• A categorification of the colored Jones polynomial at a root of unity
• Categorical relations between Langlands dual quantum affine algebras: Doubly laced types
• DG-Enhanced Hecke and KLR Algebras
• R-matrices for quantum affine algebras and Khovanov-Lauda-Rouquier algebras, I
• Young walls and graded dimension formulas for finite quiver Hecke algebras of type $A_{2\ell }^{(2)}$ and $D_{\ell +1}^{(2)}$
• Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups
• A skein relation for singular Soergel bimodules
• On level 1 cyclotomic KLR algebras of type $A_n^{(1)}$
• A geometric setting for quantum osp(1|2)
• Trace and categorical sl(n) representations
• Categorification of infinite-dimensional ${\mathfrak{sl}}_2$-modules and braid group 2-actions I: tensor products
• PBW theoretic approach to the module category of quantum affine algebras
• Suggestions to study affine and GIT quotients of the extended Grothendieck--Springer resolution
• Categorification of the adjoint action of quantum groups
• Geometric partition categories: On short Brauer algebras and their blob subalgebras
• Categorification via blocks of modular representations II
• Modified affine Hecke algebras and quiver Hecke algebras of type $A$
• Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A
• Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n
• Convolution Products and R-Matrices for KLR Algebras of Type $B$
• Monoidal categories of modules over quantum affine algebras of type A and B
• Degenerate Affine Hecke-Clifford Algebras and Type $Q$ Lie Superalgebras
• A remark on convolution products for quiver Hecke algebras
• Cyclotomic quiver Hecke algebras corresponding to minuscule representations
• Representation Theory of Symmetric Groups and Related Hecke Algebras
• Towards functor exponentiation
• Cell 2-Representations and Categorification at Prime Roots of Unity
• Faithfulness of simple 2-representations of ${\mathfrak{sl}}_2$
• Super duality for quantum affine algebras of type $A$
• Hall categories and KLR categorification
• A Categorification of the Spin Representation of $U(\mf{so}(7,\C))$ via Projective Functors
• Representations of cyclotomic oriented Brauer categories
• Type A blocks of super category O
• Cluster algebras and their bases
• Graded decomposition numbers of Ariki-Koike algebras for blocks of small weight