Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Natasha ROZHKOVSKAYA - Kansas,
Titre Construction of vertex operators from Jacobi-Trudi identities
Horaire14:00 à 15:00
RésumeThe action of algebra of fermions on the Fock space allows to construct the action on the same space of other interesting algebras, such as Heisenberg algebra, Virasoro algebra and $gl_\infty$. Boson-fermion correspondence allows to identify Fock space with boson space as modules over Heiseinberg algebra, and describes the action of algebra of fermions in terms of vertex operators (generating functions). One can notice that in this construction the crucial role is played by a property that is equivalent to the Jacobi-Trudi identity for symmetric functions. In this talk we will review the classical construction and will discuss, how more general identity can be used to construct the action algebra of fermions. This will be illustrated with examples that naturally appear in representation theory and in generalizations of symmetric functions.