Large-N limit of the generalized 2D Yang-Mills theory on cylinder

Using the collective field theory approach of large-N generalized two-dimen sional Yang-Mills theory on cylinder, it is shown that the classical equati on of motion of collective field is a generalized Hopf equation. Then, usin g the Itzykson-Zuber integral at the large-N limit, it is found that the cl assical Young tableau density, which satisfies the saddle-point equation an d determines the large-N limit of fi ee energy, is the inverse of the solut ion of this generalized Hopf equation, at a certain point. (C) 2000 Elsevie r Science B.V. All rights reserved.