Toward the Construction of Toric Imprimitive Reflection Groups (Logic, Language, Algebraic system and Related Areas in Computer Science)

Abstract

For an n-dimensional faithful imprimitive irreducible representation G → GL(V) over the complex number filed C, the ring of invariants C[V]G of G on polynomial function on V is a polynomial ring over C if and only if G is conjugate to G(m, p, n) called a finite imprimitive unitary reflection groups. We try to generalize such finite groups to affine algebraic groups with the aid of cofree covers of algebraic tori related to Gorensteinness.