On the semi-infinite cohomology and categorification of the Boson-Fermion correspondence

Abstract

In this thesis, we first examine the algebraic setting for the semi-infinite cohomology of a Lie algebra and then discuss the realization of semi-infinite cohomology by means of quantum groups. Next, we introduce the original bosonfermion correspondence and its categorification introduced by Frenkel, Penkov and Serganova. We then use the construction to categorify the Weyl algebra and Clifford algebra and their corresponding identities. Finally, we suggest possible future directions for these two topics.

Date of Award	2023
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Ivan Chi Ho IP (Supervisor)