Representations of a∞ and d∞ with central charge 1 on the single neutral fermion Fock space

21st International Conference on Integrable Systems and Quantum Symmetries

Anguelova, Iana I.^1 ; Cox, Ben^1 ; Jurisich, Elizabeth^1

Department of Mathematics, College of Charleston, Charleston, SC 29424, United States^1

关键词: Direct sum;    Fock spaces;    Highest weight modules;    Infinite ranks;    Lie Algebra;    Neutral fermions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012004/pdf
DOI  :  10.1088/1742-6596/474/1/012004

来源: IOP

【 摘 要 】

We construct a new representation of the infinite rank Lie algebra a∞with central charge c = 1 on the Fock space F⊗1/2of a single neutral fermion. We show that F⊗1/2is a direct sum of irreducible integrable highest weight modules for a∞with central charge c = 1. We prove that as a∞modules F⊗1/2is isomorphic to the Fock space F⊗1of the charged free fermions. As a corollary we obtain the decompositions of certain irreducible highest weight modules for d∞with central charge c = 1/2 into irreducible highest weight modules for d∞with central charge c = 1.