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-Lusztig polynomials.
Murata,Affine highest weight structures on module categories over quiver hecke algebras, 2024,arXiv:2412.12903
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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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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-Lusztig polynomials.
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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.