Geometric Harmonic Analysis on Homogeneous Cones and Homogeneous Siegel Domains

齐次锥体和齐次西格尔域的几何调和分析

• 批准号: 18340039
• 负责人: NOMURA Takaaki
• 金额: $ 6.82万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18340039/
• 关键词: 解析学; 関数解析学; 関数論; 幾何学; ジーゲル領域; 等質錐; ジョルダン代数; 等質開凸錐; 調和解析

There has been a conjecture concerning the gaps between the degrees of the basic relative invariants associated to homogeneous cones and the symmetry of the corresponding homogeneous tube domains (Siegel domains of the first kind).However, we found a homogeneous cone that denies the conjecture. Moreover such a cone is found in any rank greater than or equal to 3. We also discovered a homogeneous cone of arbitrary rank greater than or equal to 3 that is linearly isomorphic to its dual cone. Further, we proved that the basic relative invariants are exactly the irreducible factors of the determinant of the right multiplication operators in the complexification of the clan corresponding to the cone. In the case of symmetric cone, we computed an actual decomposition of that determinant into irreducible factors.

关于同质锥体相关的基本相对不变量的度数与相应的同质管域（第一类西格尔域）的对称性之间的差距，曾经有一个猜想。然而，我们发现了一个齐质锥体，否定了这个猜想。此外，在大于或等于 3 的任何阶中都可以找到这样的锥体。我们还发现了大于或等于 3 的任意阶的齐次锥体，它与其对偶锥体线性同构。进一步证明了基本相对不变量正是锥体对应族复化中右乘算子行列式的不可约因子。在对称圆锥的情况下，我们将该行列式实际分解为不可约因子。

项目成果

A characterization of symmetric Siegel domains by convexity of Cayley transform images

凯莱变换图像凸性表征对称西格尔域

• 发表时间: 2007
• 期刊: Tohoku Mathematical Journal 59
• 作者: K.Kitagawa;K.Ishida;R.S.Perry;H.Murakawa;K.Yoshimura;Y.Maeno;Kentaro Kitagawa;Robin S.Perry;Kenji Ishida;上尾真道;上尾真道;上尾真道;上尾真道;Chifune Kai
• 通讯作者: Chifune Kai

Wavelet transforms for semidirect product groups with not necessarily commutative normal subgroup

具有不一定可交换正态子群的半直积群的小波变换

• 发表时间: 2006
• 期刊: J. Fourier Anal. Appl. 12
• 作者: T. Kobayashi;石井志保子;重川一郎;Minoru Itoh;T. Kobayashi;T.Tomaru;熊谷隆;Hideyuki Ishi;T. Kobayashi;T. Kumagai;K.Watanabe;T. Kobayashi;Hideyuki Ishi;木上淳;T. Kobayashi;渡辺敬一;Chifune Kai;T. Kobayashi;K.Watanabe;T. Kobayashi;重川一郎;Masato Wakayama;S.Ishii;竹田雅好;T. Kobayashi;Hideyuki Ishi
• 通讯作者: Hideyuki Ishi

Unitarizability of holoraorphically induced representations of a split solvable Lie group

可解李群的全息诱导表示的幺正性

• 发表时间: 2006
• 期刊: Erwin Schrodinger Inst, Preprint 1793
• 作者: T. Kobayashi;石井志保子;重川一郎;Minoru Itoh;T. Kobayashi;T.Tomaru;熊谷隆;Hideyuki Ishi;T. Kobayashi;T. Kumagai;K.Watanabe;T. Kobayashi;Hideyuki Ishi;木上淳;T. Kobayashi;渡辺敬一;Chifune Kai;T. Kobayashi;K.Watanabe;T. Kobayashi;重川一郎;Masato Wakayama;S.Ishii;竹田雅好;T. Kobayashi;Hideyuki Ishi;K.Watanabe;日野正訓;Hideyuki Ishi
• 通讯作者: Hideyuki Ishi

Arithmetics on non-commutative harmonic oscillators

非交换简谐振子的算法

• 发表时间: 2009
• 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
• 通讯作者: Masato Wakayama

THE REPRESENTATIVE DOMAIN OF A HOMOGENEOUS BOUNDED DOMAIN

• DOI: 10.2206/kyushujm.64.35
• 发表时间: 2009
• 期刊: Kyushu Journal of Mathematics
• 影响因子: 0.4
• 作者: H. Ishi;C. Kai