Author(s):
Gatto, Letterio ; Salehyan, Parham [UNESP]
Date: 2019
Persistent ID: http://hdl.handle.net/11449/190589
Origin: Oasisbr
Subject(s): Bosonic vertex representation of Date-Jimbo-Kashiwara-Miwa; cohomology of the Grassmannian; Hasse-Schmidt derivations on exterior algebras; Schubert derivations; vertex operators; Bosonic vertex representation of Date-Jimbo-Kashiwara-Miwa; Bosonic vertex representation of Date-Jimbo-Kashiwara-Miwa; cohomology of the Grassmannian; cohomology of the Grassmannian; Hasse-Schmidt derivations on exterior algebras; Hasse-Schmidt derivations on exterior algebras; Schubert derivations; Schubert derivations; vertex operators; vertex operators
Description
Made available in DSpace on 2019-10-06T17:18:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-01-01
The integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra (Formula presented.) of all the n × n matrices with integral entries. The simplest case, r = 1, recovers the well known fact that any vector space is a module over the Lie algebra of its own endomorphisms. The other extremal case, (Formula presented.) corresponds to the bosonic vertex representation of the Lie algebra (Formula presented.) on the polynomial ring in infinitely many indeterminates, due to Date, Jimbo, Kashiwara and Miwa. In the present article we provide the structure of this irreducible representation explicitly, by means of a distinguished Hasse-Schmidt derivation on an exterior algebra, borrowed from Schubert Calculus.
Dipartimento di Scienze Matematiche Politecnico di Torino
Institute of Biosciences Humanities and Exact Sciences São Paulo State University (UNESP)
Institute of Biosciences Humanities and Exact Sciences São Paulo State University (UNESP)
