Avital Frumkin (Tel Aviv University, Israel)

Generalize diagonals products and their moments

Abstract:
   We consider the conjugacy class of the matrix with respect to the Unitarian group. For a given permutation on n elements one has a function from this orbit to the complexes given as the product of the elements of the generalize diagonal fixed by the permutation. We show that the integral of the L powers of this functions over the Unitarian group with respect to Haar measure can be expressed in term of Schur function and character of the symmetric groups on L n elements.