Character formulae and a realization of tilting modules for sl(2)[t]

Autor(es)

Bennett, Matthew ^{[1, 2]} ; Chari, Vyjayanthi ^{[1, 2]}

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil

^[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 - USA

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 441, p. 216-242, NOV 1 2015.
• Citações Web of Science: 0

Resumo

In this paper we study the category of graded modules for the current algebra associated to sl(2). The category enjoys many nice properties, including a tilting theory which was established in {[}1]. We show that the indecomposable tilting modules for sl(2){[}t] are the exterior powers of the fundamental global Weyl module and give the filtration multiplicities in the standard and costandard filtration. An interesting consequence of our result (which is far from obvious from the abstract definition) is that an indecomposable tilting module admits a free right action of the ring of symmetric polynomials in finitely many variables. Moreover, if we go modulo the augmentation ideal in this ring, the resulting sl(2){[}t]-module is isomorphic to the dual of a local Weyl module. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 13/20243-5 - Novas direções em Teoria de Lie
• Beneficiário: Matthew Lyle Bennett
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 12/06923-0 - Filtrações e propriedades homológicas de módulos graduados para álgebras de correntes e generalziações
• Beneficiário: Matthew Lyle Bennett
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado