On orbit sum values of elements of finite order

摘要

The irreducible characters form a basis of the ring of class functions on a compact, simply connected, simple Lie group. Another basis are the orbit sums φλ = Σμ∈Wλ eμ which are related to the irreducible characters by the inner multiplicities. There is a W-invariant sesquilinear form on the class functions — defined over a finite set of elements of finite order, under which the orbit sums are almost orthogonal. We give an exact criterion for the orthogonality given the set of elements of order dividing a fixed n and follow some remarkable properties of the values of orbit sums on elements of finite order (EFO).