Constructs the first rotation-invariant U_q(sl_4)-web basis via hourglass plabic graphs, crystal growth rules, and skein relations.
Light ladders and clasp conjectures
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local intersection forms attached to each summand of the tensor product of an irreducible representation with a fundamental representation. We prove this formula for n at most 4, and conjecture that it holds for all n. Given two sequences of fundamental weights which sum to the same dominant weight, the clasp is the morphism between the corresponding tensor products which projects to the top indecomposable summand. Using our computation of intersection forms, we provide a recursive, ``triple-clasp expansion'' formula for clasps. In addition, we describe the cellular structure on sl(n)-webs, and prove that sl(n)-webs are an integral form for tilting modules of quantum groups.
verdicts
UNVERDICTED 4representative citing papers
Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.
citing papers explorer
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Rotation-invariant web bases from hourglass plabic graphs
Constructs the first rotation-invariant U_q(sl_4)-web basis via hourglass plabic graphs, crystal growth rules, and skein relations.
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On a symplectic quantum Howe duality
Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.
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On Hecke and asymptotic categories for a family of complex reflection groups
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
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Orthogonal webs and semisimplification
A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.