INVARIANTS OF COMPLEX REDUCTIVE ALGEBRAIC GROUPS WITH SIMPLE COMMUTATOR SUBGROUPS

Abstract. Let G be a complex connected reductive algebraic group with simple com-mutator subgroup G′. Consider a finite dimensional representation ρ: G → GL(V) and denote by C[V]G the C-algebra consisting of polynomial functions on V which are invariant under the action of G. The purpose of this paper is to discuss on our partial classification of ρ’s such that C[V]G are polynomial rings over C. Our method is based on the property of PLH defined and studied in [9] and our study on relative equidimen-sionality of representations under the assumption that G ′ is simple. Key Words: coregular representations; relative invariants; reductive algebraic groups; algebraic tori; simple commutator subgroups; equidimensional action