A new character formula for Lie algebras and Lie groups (Q2905193)

The effective determination of characters for Lie groups and Lie algebras is a very important work. A series of methods for determining of these have been proposed by a number of mathematical physicists, e.g. Hermann Weyl, Élie Cartan, Issai Schur, Richard Brauer and Hans Freudenthal, etc.. The study of the method for determining the characters is a very meaningful work. In this article, the author gives a new character formula for finite-dimensional representations of finite-dimensional complex semisimple Lie algebras and compact semisimple Lie groups which seems to be very different from previously-known formulas. The author also proves a few consequences and applications include new recursion formulas for multiplicities.