Lectures on integrable hierarchies and vertex operators
A.A.Vladimirov
TL;DR
This paper provides an educational overview of integrable hierarchies, vertex operators, and related algebraic structures, aimed at graduate students, covering foundational concepts and their interrelations.
Contribution
It offers a comprehensive, accessible introduction to integrable systems, fermionic and bosonic formalisms, and vertex algebras, connecting these topics for the first time in a pedagogical manner.
Findings
Clarifies the scalar Ansatz in KP hierarchy
Explains fermionic Fock space and Fermi-Bose correspondence
Details the role of vertex algebras and operator product expansion
Abstract
This is a write-up of lectures intended for (under)graduate students. Contents: Scalar Ansatz (KP hierarchy). Fermionic Fock space. Fermi-Bose correspondence. KP hierarchy via free fermions. Formal distributions and locality. Operator product expansion. Vertex algebras. Free fermions. Virasoro algebra in KdV.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra