On a class of multiplicity-free nilpotent K_C-orbits

Details On a class of multiplicity-free nilpotent K_C-orbits On a class of multiplicity-free nilpotent K_C-orbits

2006-08-07

arxiv.org/abs/math/0608167v6

Mathematics

Representation Theory

Version accepted for publication in the J. Math. of Kyoto Univ. (with revised abstract, added references, and typos corrected)

Scientific paper

Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal noncompact weights are constructed and classified for each real noncompact simple Lie group of classical type. We show that for each partial subsequence there is a corresponding family of K_C-orbits, ordered by inclusion and such that the representation of K on the ring of regular functions on the closure of the orbit is multiplicity-free. The K-types of regular functions on the orbits and the regular functions on their closures are both explicitly identified and demonstrated to coincide, with one exception in the Hermitian symmetric case. The classification presented also includes the specification of a base point for each orbit and exhibits a corresponding system of restricted roots with multiplicities. A formula for the leading term of the Hilbert polynomials corresponding to these orbits is given. This formula, together with the restricted root data, allows the determination of the dimensions of these orbits and the algebraic-geometric degree of their closures. In an appendix, the location of these orbits within D. King's classification of spherical nilpotent orbits in complex symmetric spaces is depicted via signed partitions and Hasse diagrams.

Affiliated with

Also associated with

No associations

Rating

On a class of multiplicity-free nilpotent K_C-orbits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a class of multiplicity-free nilpotent K_C-orbits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a class of multiplicity-free nilpotent K_C-orbits will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-601483