Author(s):
Gatto, Letterio ; Salehyan, Parham [UNESP]
Date: 2020
Persistent ID: http://hdl.handle.net/11449/201520
Origin: Oasisbr
Subject(s): Bosonic and Fermionic Fock spaces; Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa; Hasse–Schmidt derivations on exterior algebras; Schubert derivations on infinite wedge powers; Vertex operators; Bosonic and Fermionic Fock spaces; Bosonic and Fermionic Fock spaces; Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa; Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa; Hasse–Schmidt derivations on exterior algebras; Hasse–Schmidt derivations on exterior algebras; Schubert derivations on infinite wedge powers; Schubert derivations on infinite wedge powers; Vertex operators; Vertex operators
Description
Made available in DSpace on 2020-12-12T02:34:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01
The Schubert derivation is a distinguished Hasse–Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert derivation to the infinite exterior power of a free Z-module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the integration by parts formula, that also recovers the generating function occurring in the bosonic vertex representation of the Lie algebra gl∞(Z) , due to Date, Jimbo, Kashiwara and Miwa (DJKM). In the present framework, the DJKM result will be interpreted as a limit case of the following general observation: the singular cohomology of the complex Grassmannian G(r, n) is an irreducible representation of the Lie algebra of n× n square matrices.
Dipartimento di Scienze Matematiche Politecnico di Torino
Ibilce UNESP, Campus de São José do Rio Preto
Ibilce UNESP, Campus de São José do Rio Preto
