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arxiv: 2309.14481 · v1 · pith:7QNMPPZUnew · submitted 2023-09-25 · 🧮 math.CO · math.RT

Strange Expectations in Affine Weyl Groups

classification 🧮 math.CO math.RT
keywords typeaffinecoregroupssimultaneousweyladditionappropriate
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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

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Core abaci and Diophantine equations I: fundamental weight

    math.NT 2026-04 unverdicted novelty 7.0

    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...

  2. Core abaci and Diophantine equations I: fundamental weight

    math.NT 2026-04 unverdicted novelty 7.0

    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...