The degrees of orbits of the multiplicity-free actions (Q2740891)

Let \(K\) be a connected reductive complex algebraic group. In the present paper, the authors give a formula for the degrees of orbits of an irreducible representation \(V\) with multiplicity-free action (i.e., any irreducible representation of \(K\) occurs at most once in the polynomial ring \(C[V]\)). In particular, the Bernstein degree and the associated cycle of the irreducible unitary highest weight modules of the scalar type are determined for arbitrary hermitian Lie algebras.NEWLINENEWLINEFor the entire collection see [Zbl 0968.22001].