Partitions, vertex operator constructions and multi-component KP equations

Maarten Bergvelt and A. P. E. ten Kroode

Vol. 171 (1995), No. 1, 23–88

DOI: 10.2140/pjm.1995.171.23

Abstract

For every partition of a positive integer n in k parts and every point of an infinite Grassmannian we obtain a solution of the k component differential-difference KP hierarchy and a corresponding Baker function. A partition of n also determines a vertex operator construction of the fundamental representations of the infinite matrix algebra gl_∞ and hence a τ function. We use these fundamental representations to study the Gauss decomposition in the infinite matrix group Gl_∞ and to express the Baker function in terms of τ-functions. The reduction to loop algebras is discussed.

Mathematical Subject Classification 2000

Primary: 58F07

Secondary: 17B65, 35Q53

Milestones

Received: 19 February 1993

Revised: 27 September 1993

Published: 1 November 1995