A Categorification of the Boson-Fermion Correspondence via Representation Theory of sl(infinity)

作者：Frenkel Igor^*; Penkov Ivan^*; Serganova Vera^*

来源：Communications in Mathematical Physics, 2016, 341(3): 911-931.

DOI：10.1007/s00220-015-2491-9

In recent years different aspects of categorification of the boson-fermion correspondence have been studied. In this paper we propose a categorification of the boson-fermion correspondence based on the category of tensor modules of the Lie algebra sl(a) of finitary infinite matrices. By we denote the category of "polynomial" tensor sl(a)-modules. There is a natural "creation" functor , . The key idea of the paper is to employ the entire category of tensor sl(a)-modules in order to define the "annihilation" functor corresponding to . We show that the relations allowing one to express fermions via bosons arise from relations in the cohomology of complexes of linear endofunctors on T+.

• 出版日期2016-2