Une conjecture du deuxième auteur, qui a été prouvée par Bonnafé–Rouquier, dit que la matrice de multiplicité des bébé modules de Verma de l’algèbre rationnelle restreinte de Cherednik est de rang un sur
Dans cet article nous montrons que si
En particulier, puisque la matrice de multiplicité pour les algèbres de Cherednik rationnelles restreintes a la propriété de rang un si et seulement si sa matrice de Cartan l’a aussi, notre résultat fournit une preuve différente de la conjecture originale.
A conjecture by the second author, proven by Bonnafé–Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one over
In this paper, we show that if
In particular, since the multiplicity matrix for restricted rational Cherednik algebras has the rank-one property if and only if its Cartan matrix does, our result provides a different proof of the original conjecture.
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Gwyn Bellamy 1 ; Ulrich Thiel 2

@article{CRMATH_2023__361_G8_1341_0, author = {Gwyn Bellamy and Ulrich Thiel}, title = {The {Rank-One} property for free {Frobenius} extensions}, journal = {Comptes Rendus. Math\'ematique}, pages = {1341--1348}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.502}, language = {en}, }
Gwyn Bellamy; Ulrich Thiel. The Rank-One property for free Frobenius extensions. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1341-1348. doi : 10.5802/crmath.502. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.502/
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