Visible actions on irreducible multiplicity-free spaces
Visible actions on irreducible multiplicity-free spaces
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不可约重数自由空间上的可见动作
DOI：
10.3792/pjaa.83.109
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. Sasaki
中科院分区：
文献类型：
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作者：
A. Sasaki
李群G在复流形D上的全纯作用称为强可见的，如果存在一个全真实的子流形S满足D中的每个G-轨道和一个反全纯同构σ使得σ s = id s且a保持每个G-轨道.本文证明了Kac的无重数空间是强可见的，即如果（G c，V）是复约化李群G c的不可约无重数空间，则G c的紧致真实的形式以强可见的方式作用于V。此外，我们给出了全真实的子流形S和反全纯对合σ的选择的明确描述。这证明了小林的猜想[8，猜想3.2]，即dim RS与GC在C[V]上的多项式表示的秩一致.
A holomorphic action of a Lie group G on a complex manifold D is called strongly visible if there exist a totally real submanifold S which meets every G-orbit in D and an anti-holomorphic diffeomorphism σ such that σ\s = id s and a preserves every G-orbit. In this paper, we prove that Kac's multiplicity-free space is strongly visible, that is, if (G c , V) is an irreducible multiplicity-free space of a complex reductive Lie group G c , then a compact real form of G c acts on V in a strongly visible fashion. Furthermore, we give an explicit description of the choice of a totally real submanifold S and an anti-holomorphic involution σ. This gives an evidence to Kobayashi's conjecture [8, Conjecture 3.2] , that is, dim R S coincides with the rank of the polynomial representation of G c on C[V] in this setting.
DOI：
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发表时间：
2006
期刊：
影响因子：
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作者：
阿原一志;石井志保子;伊藤哲史;伊藤由佳理;牛瀧文宏;大栗博司;他全20名;相川弘明;Hidenori Fujiwara;T. Kobayashi;Takaaki Nomura;T. Kobayashi;Takaaki Nomura;T. Kobayashi;Masato Wakayama;T. Kobayashi;T. Kobayashi;Takaaki Nomura;Takaaki Nomura;T. Kobayashi;Hideyuki Ishi;Hidenori Fujiwara;T.Kobayashi;Minoru Itoh;T.Kobayashi;Chifune Kai;T.Kobayashi;T.Kobayashi;T.Kobayashi;Hideyuki Ishi;T.Kobayashi;Takaaki Nomura;T. Kobayashi
通讯作者：
T. Kobayashi