Raising operators for the Whittaker wave functions of the Toda chain and intertwining operators

Intertwiners between representations of Lie groups can be used for obtaining relations for matrix elements. We apply this technique to obtain different identities for the wave functions of the open Toda chain, in particular, raising operators and bilinear relations for the wave functions on different energy levels. We also recall the group-theory approach to the Toda chain: treating the wave functions as matrix elements in irreducible representations between the so-called Whittaker vectors, integral representations of the wave functions, etc. © 2005 Springer Science+Business Media, Inc.