Generalised core partitions and Diophantine equations
Résumé
We study generalised core partitions arising from affine Grassmannian
elements in arbitrary Dynkin type. The corresponding notion of size is given by
the atomic length in the sense of [CLG22]. In this paper, we first develop the
theory for extended affine Weyl groups. In a series of applications, we give
some remarkable parametrisations of the solutions of certain Diophantine
equations resembling Pell's equation, by refining the results of [BN22] and
[Alp14], and generalising them to further types.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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