2003/12/25 by Kyo Nishiyama, Hiroyuki Ochiai, Chen-Bo Zhu +1 · 16 citations
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced NMR Techniques and Applications #Algebraic structures and combinatorial models #Closure (psychology) #Combinatorics #Discrete mathematics #Hermitian matrix #Mathematics #Nilpotent #Orbit (dynamics) #Pure mathematics #Ring (chemistry) #math.AG #math.RT #msc:11F27 #msc:22E46
paper · pdf · doi:10.1090/s0002-9947-05-03826-2
published in Transactions of the American Mathematical Society 358(6), 2713-2734 (American Mathematical Society) · 26 pages
arxiv created 2003/12/25 · openalex publication_date 2005/12/20 · arxiv updated 2010/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a reductive dual pair (G, Gâ) in the stable range with Gâ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent Kâ_\mathbb C-orbits, where Kâ is a maximal compact subgroup of Gâ and we describe the precise K_\mathbb C-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair ( G, K). As an application, we prove sphericality and normality of the closure of certain nilpotent K_\mathbb C-orbits obtained in this way. We also give integral formulas for their degrees.