INTEGRABLE MODULES FOR AFFINE LIE SUPERALGEBRAS

Autor(es)

Rao, Senapathi Eswara ^[1] ; Futorny, Vyacheslav ^[2]

Afiliação do(s) autor(es)

^[1] Tata Inst Fundamental Res, Bombay 400005, Maharashtra - India

^[2] Univ Sao Paulo, Inst Math, BR-05315970 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 361, n. 10, p. 5435-5455, OCT 2009.
• Citações Web of Science: 3

Resumo

Irreducible nonzero level modules with finite-dimensional weight spaces are discussed for nontwisted affine Lie superalgebras. A complete classification of such modules is obtained for superalgebras of type A(m, n)(boolean AND) and C(n)(boolean AND) using Mathieu's classification of cuspidal modules over simple Lie algebras. In other cases the classification problem is reduced to the classification of cuspidal modules over finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu and Penkov. Based on these results a. complete classification of irreducible integrable (in the sense of Kac and Wakimoto) modules is obtained by showing that any such module is of highest weight, in which case the problem was solved by Kac and Wakimoto. (AU)

• Processo FAPESP: 05/60337-2 - Álgebras de Lie e de Jordan, suas representações e generalizações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático