Uniform Fock space constructions and Virasoro characterizations yield level-rank dualities for classical affine Lie algebras and interpret KLR algebra defects via moving vectors.
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Core abaci of arbitrary charge parameterize the affine Grassmannian and equate the height of weights to atomic lengths of Weyl elements, solving a generalized open problem and parameterizing solutions to certain Diophantine equations via Uglov vectors.
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Level-rank dualities and moving vectors
Uniform Fock space constructions and Virasoro characterizations yield level-rank dualities for classical affine Lie algebras and interpret KLR algebra defects via moving vectors.
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Core abaci and Diophantine equations I: fundamental weight
Core abaci of arbitrary charge parameterize the affine Grassmannian and equate the height of weights to atomic lengths of Weyl elements, solving a generalized open problem and parameterizing solutions to certain Diophantine equations via Uglov vectors.