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Bosonic and fermionic representations of endomorphisms of exterior algebras

Volume 256 / 2022

Ommolbanin Behzad, Letterio Gatto 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.

Authors

  • Ommolbanin BehzadDepartment of Pure Mathematics Faculty of Mathematics and Statistics
    University of Isfahan
    P.O. Box 81746-73441
    Isfahan, Iran
    e-mail
  • Letterio GattoDipartimento di Scienze Matematiche
    Politecnico di Torino
    Corso Duca degli Abruzzi 24
    10129 Torino, Italy
    e-mail

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