# Untitled

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0506.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**On a Gauss-Givental Representation of Quantum Toda
Chain Wave Function**

We propose group theory interpretation of the integral
representation of the quantum open Toda chain wave function due to
Givental. In particular we construct the representation of
$U(\mathfrak{gl}(N))$ in terms of first order differential operators
in Givental variables. The construction of this representation turns out
to be
closely connected with the integral representation based on the
factorized Gauss decomposition. We also reveal the recursive structure
of the Givental representation and provide the connection
with the Baxter $Q$-operator formalism. Finally the generalization of the
integral representation to the
infinite and periodic quantum Toda wave functions
is discussed.