An Adjoint Quotient for Certain Groups Attached to Kac-Moody Algebras

摘要: In this article we want to give a survey of that part our Habilitationsschrift [16] which deals with conjugacy classes in certain groups G attached Kac-Moody Lie algebras. These investigations were motivated on one side by the result Brieskorn relating simple singularities and algebraic (see for instance [14]) other recent results Looijenga deformation theory simply elliptic cusp ([9], [10]). The show at least some extent there is similar relationship between these associated as groups. Here, shall limit ourselves group-theoretical aspects, i.e. definition (due E. Looijenga) an adjoint quotient arbitrary group analyze structure its fibers. A large notes will be dedicated explanation Looijenga’s “partial compactification” T/W maximal torus T Weyl W since space figure base G. Its stratification into boundary components induces partition can described terms building We conjecture representation-theoretic interpretation seems relevant when dealing character-theoretic construction quotient. Some open problems direction are mentioned end. Detailed proofs may found [16]. There also relations explained.