Orbits and Invariants of Super Weyl Groupoid

Abstract

We study the orbits and polynomial invariants of certain affine action of the super Weyl groupoid of Lie superalgebra gl(n,m), depending on a parameter. We show that for generic values of the parameter all the orbits are finite and separated by certain explicitly given invariants. We also describe explicitly the special set of parameters, for which the algebra of invariants is not finitely generated and does not separate the orbits, some of which are infinite.