Unitary structure in representations of infinite-dimensional groups and a convexity theorem

摘要: In this paper, we show that a Kac-Moody algebra fl(A) associated to symmetrizable generalized Cartan matrix A carries contravariant Hermitian form which is positive-definite on all root spaces. We deduce every integrable highest weight g(A)-module L(A) positivedefinite form. This allows us define the moment map and prove generalization of Schur-Horn-Kosta nt-Heckman-Atiya h-Pressley convexity theorem. The proofs are based an identity also gives estimates for action 9(A) L(A). hope main idea behind paper apparent: it use interplay between coadjoint representations. grateful V. Guillemin introduction map.