Schubert Derivations on the Infinite Wedge Power

Autor: Parham Salehyan, Letterio Gatto
Přispěvatelé: Politecnico di Torino, Universidade Estadual Paulista (Unesp)
Rok vydání: 2019
Předmět:
Pure mathematics
infinite wedge powers
Bosonic and Fermionic Fock spaces
General Mathematics
Schubert calculus
FOS: Physical sciences
Fock space
Mathematics - Algebraic Geometry
Grassmannian
Mathematics::Quantum Algebra
Lie algebra
FOS: Mathematics
14M15
15A75
05E05
17B69
Mathematics - Combinatorics
Representation Theory (math.RT)
Mathematics::Representation Theory
Exterior algebra
Algebraic Geometry (math.AG)
Mathematical Physics
Mathematics
Vertex operators
Hasse–Schmidt derivations on exterior algebras
Bosonic vertex representation of Date Jimbo Kashiwara Miwa
Schubert derivations on infinite wedge powers
Hasse Schmidt derivations on exterior algebras
Mathematical Physics (math-ph)
Cohomology
Free abelian group
Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa
Irreducible representation
Schubert derivations on
Combinatorics (math.CO)
Mathematics - Representation Theory
Zdroj: Scopus
Repositório Institucional da UNESP
Universidade Estadual Paulista (UNESP)
instacron:UNESP
DOI: 10.48550/arxiv.1901.06853
Popis: The {\em 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 ${\mathbb Z}$-module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the {\em integration by parts formula}, that also recovers the generating function occurring in the {\em bosonic vertex representation} of the Lie algebra $gl_\infty({\mathbb Z})$, 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 $n\times n$ square matrices.}
Comment: 23 pages, no figures, comments welcome. Few typos corrected and updated reference list
Databáze: OpenAIRE
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