  We study the semi-discrete directed random polymer model introduced by
O'Connell and Yor. We obtain a representation for the moment generating
function of the polymer partition function in terms of a determinantal measure.
This measure is an extension of the probability measure of the eigenvalues for
the Gaussian Unitary Ensemble (GUE) in random matrix theory. To establish the
relation, we introduce another determinantal measure on larger degrees of
freedom and consider its few properties, from which the representation above
follows immediately.
