Singular characters and their Lp-norms on classical Lie groups

We show that the Weyl's characters formula takes a particular form in the case of representations whose maximal weight is singular. This formula enables us to prove the following statement. Let G be a compact connected Lie group such that the complexification of its Lie algebra is a direct sum of its center with classical Lie algebras; then there exists a sequence {\u3bb_n} in the dual object G such that their dimension tends to infinity, tends to infinity and the L^p norm of their characters is uniformly bounded