Algebra Seminar

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.