Comultiplication in ABCD algebra and scalar products of Bethe wave functions

Abstract

The representation of scalar products of Bethe wave functions in terms of the Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in \cite{Izergin87} and \cite{Korepin87} is based on the explicit expression for the "senior" coefficient which was guessed in \cite{Izergin87} and then proven to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on the direct computation.Comment: 9 page