Partitions, vertex operator constructions and multi-component KP equations

Maarten Bergvelt, A. ten Kroode
1995 Pacific Journal of Mathematics  
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 r function. We use these fundamental representations to study the Gauss decomposition in the infinite matrix group Gloo and to express the
more » ... er function in terms of r-functions. The reduction to loop algebras is discussed.
doi:10.2140/pjm.1995.171.23 fatcat:ad57x5umxfgfzfywmoofjsfayi