Strange Expectations in Affine Weyl Groups
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Our main result is a generalization, to all affine Weyl groups, of P. Johnson's proof of D. Armstrong's conjecture for the expected number of boxes in a simultaneous core. This extends earlier results by the second and third authors in simply-laced type. We do this by modifying and refining the appropriate notion of the "size" of a simultaneous core. In addition, we provide combinatorial core-like models for the coroot lattices in classical type and type $G_2$.
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Cited by 2 Pith papers
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Core abaci and Diophantine equations I: fundamental weight
Core abaci of arbitrary charge parameterize affine Grassmannians and equate the height of β to the atomic length of the corresponding Weyl group element w_λ,j, solving a generalized open problem and yielding closed fo...
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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 Dioph...
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