2011/08/30 by Yuly Billig, Vyacheslav Futorny, Billig, Yuly +1
Mathematics · Physics and Astronomy · #17B66 #17B67 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1108.6092
openalex publication_date 2011/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to study the representation theory of a classical\ninfinite-dimensional Lie algebra - the Lie algebra of vector fields on an\nN-dimensional torus for N > 1. The case N=1 gives a famous Virasoro algebra (or\nits centerless version - the Witt algebra). The algebra of vector fields has an\nimportant class of tensor modules parametrized by finite-dimensional modules of\ngl(N). Tensor modules can be used in turn to construct bounded irreducible\nmodules for the vector fields on N+1-dimensional torus, which are the central\nobjects of our study. We solve two problems regarding these bounded modules: we\nconstruct their free field realizations and determine their characters. To\nsolve these problems we analyze the structure of the irreducible modules for\nthe semidirect product of vector fields with the quotient of 1-forms by the\ndifferentials of functions. These modules remain irreducible when restricted to\nthe subalgebra of vector fields, unless they belongs to the chiral de Rham\ncomplex, introduced by Malikov-Schechtman-Vaintrob.\n