| Texto completo | |
| Autor(es): |
Billig, Yuly
;
Futorny, Vyacheslav
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 366, n. 9, p. 35-pg., 2014-09-01. |
| Resumo | |
The goal of this paper is to study the representation theory of a classical infinite-dimensional Lie algebra - the Lie algebra VectT(N) of vector fields on an N-dimensional torus for N > 1. The case N = 1 gives a famous Virasoro algebra (or its centerless version -the Witt algebra). The algebra VectT(N) has a natural class of tensor modules parametrized by finitedimensional modules of gl(N). Tensor modules can be used in turn to construct bounded irreducible modules for VectT(N+1) (induced from VectT(N)), which are the focus of our study. We solve two problems regarding these bounded modules: we construct their free field realizations and determine their characters. To solve these problems we analyze the structure of the irreducible Omega(1) (TN+1) / d Omega(0) (TN+1)x VectT(N+1)-modules constructed in a paper by the first author. These modules remain irreducible when restricted to the subalgebra VectT(N+1), unless they belong to the chiral de Rham complex, introduced by Malikov-Schechtman-Vaintrob (1999). (AU) | |
| Processo FAPESP: | 08/10471-2 - Yuly Billig | Universidade de Carleton - Canadá |
| Beneficiário: | Vyacheslav Futorny |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Internacional |