Schubert Derivations on the Infinite Wedge Power

Author(s)

Gatto, Letterio ^[1] ; Salehyan, Parham ^[2]

Affiliation

^[1] Politecn Torino, Dipartimento Sci Matemat, Turin - Italy

^[2] Ibilce UNESP, Campus Sao Jose Do Rio Preto, Sao Jose Do Rio Preto, SP - Brazil

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 52, n. 1 JAN 2020.
• Web of Science Citations: 1

Abstract

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 freeZ-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 gl8(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 x n square matrices. (AU)

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