Geometric invariant theory and the generalized eigenvalue problem

• 成果类型: Article
• 署名作者: Ressayre, N.
• 署名单位: Universite de Montpellier
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0233-3
• 发表日期: 2010
• 页码: 389-441
• 关键词: honeycomb model; Orbits; PROOF; saturation; polytopes

摘要

Let G be a connected reductive subgroup of a complex connected reductive group (G) over cap. Fix maximal tori and Borel subgroups of G and (G) over cap. Consider the cone LR( G, (G) over cap) generated by the pairs (v, (v) over cap) of dominant characters such that V-v*. is a submodule of V (v) over cap. ( with usual notation). Here we give a minimal set of inequalities describing LR(G, (G) over cap) as a part of the dominant chamber. In other words, we describe the facets of LR(G, (G) over cap) which intersect the interior of the dominant chamber. We also describe smaller faces. Finally, we are interested in some classical redundant inequalities. Along the way, we obtain results about the faces of the Dolgachev-Hu G-ample cone and variations of this cone.