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2-Kac-Moody algebras
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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.
Forward citations
Cited by 10 Pith papers
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2-categorical affine symmetries of quantum enveloping algebras
Constructs 2-representations of affine quantum enveloping algebras on finite-dimensional versions in type A_n and proves prefundamental character formulas using quotients and evaluation morphisms.
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Monoidal Jantzen filtrations
Monoidal Jantzen filtrations induce an associative deformation of Grothendieck ring multiplication that quantizes the ring and recovers known quantum versions in representation categories of quantum loop algebras and ...
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Rewriting modulo isotopies in Khovanov-Lauda-Rouquier's categorification of quantum groups
Rewriting modulo isotopies computes bases for 2-cells in the KLR 2-category that match Khovanov-Lauda conjectures, proving non-degeneracy and thus categorification of Lusztig's integral quantum group.
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Quantum imaginary Schur-Weyl duality
Proves a parameter-dependent deformation of imaginary Schur-Weyl duality for affine type A quiver Hecke algebras and derives character formulas for simple and standard modules using dual canonical bases and Kazhdan-Lu...
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Kleshchev multipartitions, affine Mirkovi\'c-Vilonen polytopes, and representations of KLR algebras in type ${\tt A}^{(1)}_1$
Explicit isomorphisms are built between three models of the B(∞) crystal in type A1^(1), including a new upper ledge diagram model, plus applications to KLR algebra branching rules.
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Quiver Hecke--Clifford superalgebras and R-matrices
Develops foundations of quiver Hecke-Clifford superalgebras and constructs Schur-Weyl duality for quantum affine queer Lie superalgebras with type A versions based on Kwon-Lee.
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Natural transformations between braiding functors in the Fukaya category
Computes all cohomologically distinct A_∞-natural transformations Nat(id, id) and Nat(id, β_i^-) in the Fukaya category of the sl_2 Coulomb branch and classifies them via Hochschild cohomology from a Chouhy-Solotar re...
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Canonical bases of tensor products and positivity properties
A thickening realization reduces canonical basis transition matrices and structure constants for tensor products in quantum groups to those of a larger quantum group's negative part, implying positivity.
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Quiver Schur algebras and cohomological Hall algebras
Quiver Schur algebras are realized as operator algebras on cohomological Hall algebras, with shuffle descriptions reinterpreted using Demazure operators, plus results on mixed versions and geometric realizations of mo...
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Resolutions of standard modules over KLR algebras of type $A$
Constructs explicit projective resolutions of standard modules Δ(π) over KLR algebras of type A.
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