タニグチ　ケンジ   TANIGUCHI Kenji   谷口　健二    所属   青山学院大学  理工学部 数理サイエンス学科    職種   教授
言語種別	英語
発行・発表の年月	2014/03
形態種別	学術雑誌
査読	査読あり
標題	Closed orbits on partial flag varieties and double flag variety of finite type
執筆形態	共同
巻・号・頁	pp.113-119
著者・共著者	Kensuke Kondo, Kyo Nishiyama, Hiroyuki Ochiai
概要	Let G be a connected reductive algebraic group over C. We denote by K=(Gθ)0 the identity component of the fixed points of an involutive automorphism θ of G. The pair (G,K) is called a symmetric pair. Let Q be a parabolic subgroup of K. We want to find a pair of parabolic subgroups P1, P2 of G such that (i) P1 ∩ P2 = Q and (ii) P1 P2 is dense in G. The main result of this article states that, for a simple group G, we can find such a pair if and only if (G,K) is a Hermitian symmetric pair. The conditions (i) and (ii) imply that the K-orbit through the origin (eP1,eP2) of G/P1 × G/P2 is closed and it generates an open dense G-orbit on the product of partial flag variety. From this point of view, we also give a complete classification of closed orbits on G/P1 × G/P2.