Complexity and rank of homogeneous spaces

✍ Scribed by D. I. Panyushev

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 917 KB
• Volume: 34
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181688

✦ Synopsis

We study an algebraic varieties with the action ofa reductive group G. The relation is elucidated between the notions of complexity and rank of an arbitrary G-variety and the structure of stabilizers of general position of some actions of G itself and its Borel subgroup. The application of this theory to homogeneous spaces provides the explicit formulas for the rank and the complexity of quasiafline G/H in terms of co-isotropy representation of H. The existence of Cartan subspace (and hence the freeness of algebra of invariants) for co-isotropy representation of a connected observable spherical subgroup H is proved.