Geometric invariant theory and generalized eigenvalue problem. II (Q407792)

This paper is a follow up to the earlier paper of the same author [Invent. Math. 180, No. 2, 389--441 (2010; Zbl 1197.14051)], and the notation here follows the earlier review. In particular, \(G\subseteq \hat G\) are complex connected reductive groups.NEWLINENEWLINEIn the first paper, the author gave a set of inequalities describing the facets of the cone \(\mathcal{LR}(G,\hat G)\) and some information describing the smaller faces. In the paper under review, the author goes further, giving a complete parametrization of the faces of the cone \(\mathcal{LR}^\circ(G,\hat G)\) (here \(\mathcal{LR}^\circ(G,\hat G)\) is generated by pairs of stricly dominant characters rather than dominant characters). One can also use the parametrization given to work out inclusion amongst the faces. The results, which rely on GIT methods, come as special cases of general results about cones coming from Geometric Invariant Theory.