University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Grigori Olshanski
    Dobrushin Mathematics Laboratory, Institute for Information Transmission Problems, Moscow

    Dimensions of skew Young diagrams and Frobenius-Schur functions.

    Friday 16th April, 12-1pm, Carslaw 375.

    I will report on a recent joint work with A.Regev and A.Vershik. We introduce and study a new family of symmetric functions -- the so-called Frobenius-Schur functions. These functions form an inhomogeneous basis in the algebra of symmetric functions. They give a solution to an interpolation problem and have many interesting properties. As an application, a formula for the combinatorial dimension of a skew Young diagram will be presented. This formula is very useful in studying asymptotic properties of characters of large symmetric groups.