Bosonic and fermionic representations of endomorphisms of exterior algebras
Volume 256 / 2022
Fundamenta Mathematicae 256 (2022), 307-331
MSC: Primary 15A75; Secondary 17B69, 14M15, 05E05.
DOI: 10.4064/fm9-12-2020
Published online: 7 September 2021
Abstract
We describe the fermionic and bosonic Fock representations of endomorphisms of the exterior algebra of a $\mathbb Q $-vector space of infinite countable dimension. Our main tool is the extension of Schubert derivations, some distinguished kind of Hasse–Schmidt derivations originally defined for exterior algebras only, to the fermionic Fock space.
