University of Sydney
School of Mathematics and Statistics
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.