On truncated Weyl modules

Autor(es)

Fourier, Ghislain ^[1] ; Martins, Victor ^[2] ; Moura, Adriano ^[3]

Afiliação do(s) autor(es)

^[1] Leibniz Univ Hannover, Inst Algebra Zahlentheorie & Diskrete Math, Hannover - Germany

^[2] Univ Fed Espirito, CCENS, Dept Matemat & Pura Aplicada, Santo Alegre - Brazil

^[3] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 47, n. 3, p. 1125-1146, MAR 4 2019.
• Citações Web of Science: 0

Resumo

We study structural properties of truncated Weyl modules. A truncated Weyl module is a local Weyl module for , where is a finite-dimensional simple Lie algebra. It has been conjectured that, if N is sufficiently small with respect to lambda, the truncated Weyl module is isomorphic to a fusion product of certain irreducible modules. Our main result proves this conjecture when lambda is a multiple of certain fundamental weights, including all minuscule ones for simply laced . We also take a further step towards proving the conjecture for all multiples of fundamental weights by proving that the corresponding truncated Weyl module is isomorphic to a natural quotient of a fusion product of Kirillov-Reshetikhin modules. One important part of the proof of the main result shows that any truncated Weyl module is isomorphic to a Chari-Venkatesh module and explicitly describes the corresponding family of partitions. This leads to further results in the case that related to Demazure flags and chains of inclusions of truncated Weyl modules. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático