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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The cohomology of the Grassmannian is a gl(n)-module

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Gatto, Letterio [1] ; Salehyan, Parham [2]
Total Authors: 2
[1] Politecn Torino, Dipartimento Sci Matemat, Turin - Italy
[2] Sao Paulo State Univ UNESP, Inst Biosci Humanities & Exact Sci, Sao Jose Do Rio Preto - Brazil
Total Affiliations: 2
Document type: Journal article
Web of Science Citations: 0

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 of all the n x 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, corresponds to the bosonic vertex representation of the Lie algebra 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 (AU)

FAPESP's process: 16/03161-3 - Hasse-Schmidt derivations tools for algebra and algebraic geometry
Grantee:Parham Salehyan
Support type: Research Grants - Visiting Researcher Grant - International