Weyl群の射影表現と超Lie代数の表現の組合せ論的構造の研究

Weyl群射影表示与超李代数表示的组合结构研究

• 批准号: 12740024
• 负责人: 山口 学
• 金额: $ 1.41万
• 依托单位: Aoyama Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Encouragement of Young Scientists (A)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12740024/
• 关键词: Clifford代数; 射影表現; 双対対; 対象群; 超Lie代数; B型Wey1群; 対称群; B型Weyl群

超Lie代数の自然表現のテンソル積表現上に双対対を構成する問題において,とくにqueer Lie superalgebraと呼ばれる超Lie代数の場合を研究したすでに,対称群の射影表現との双対対を構成している,この結果は,テンソル積表現全空間における制限則を与える(全空間ではB型Wey1群の射影表現(ある2-cocycleに対するもの)と双対対をなす(A. N. Sergeev)).証明の途中で:B型Wey1群のこのタイプの射影表現がClifford代数の通常表現と対称群の射影表現とのZ/2Z-gradedなテンソル積を用いて構成できることを示した.今年度は,queer Lie superalgebra2つの直和の通常表現とB型Weyl群の射影表現(Sergeevの場合とは異なる2-cocycleに対するもの)とが双対対をなすことを証明した.証明の途中でB型Wey1群のこの2-cocycleに対する振れ群環が可換群Z/2Zと対称群のねじれ群環との"レス積のような"構造をもつことを示した.そして既約射影表現をlittle group methodと類似の方法で構成した.また,上述の2つの2-cocycleと異なるもう一つの2-Cocycleに対してB型Weyl群の射影表現を構成した,この場合,既約表現はClifford代数の通常表現と対称群の射影表現とのnongradedなテンソル積によって構成される.さらに,このB型Wey1群の射影表現と超Lie代数との双対対の構成した.

The active table of super-Lie algebra naturally shows that the problem is now known as a problem, and queer Lie superalgebra calls for the combination of super-Lie algebras to study the problem, and the group projective table shows that the double signals are broken, and the results are good. Full space traffic restrictions and restrictions are available (full space transmission B Wey1 group projection display) dual transmission transmission (A. N. Sergeev). On the way: the projective representation of the Wey1 group of type B shows that the Clifford algebra usually shows that the group is called the group. The projective representation of the Z/2Z-graded group shows that it actively shows that it is called a group. This year, queer Lie superalgebra2 has shown that the B-type Weyl group projective display (Sergeev, combination, 2-cocycle, etc.) usually shows that the B-type projective image is accurate. On the way to Ming, the B-type Wey1 group may be called the group ZUnip 2Z, and the group may be called the group. The group may be called the group. The group may be called the group. The original projective table shows that the little group method type is similar to that of the method. The projective representation of the type B Weyl group of the above-mentioned 2-cocycle algebras usually shows that the Clifford algebra is the same as that of the nongraded algebras. The projective representation of the Wey1 group of type B shows that the super-Lie algebra is bipolar.

项目成果

Manabu Yamaguchi: "A duality of a twisted group algebra of the hyperoctahedral group and the queer Lie superalgebra"Advanced Studies in Pure Mathematics Combinatorial Methods in Representation Theory. 28. 401-422 (2000)

Manabu Yamaguchi：“超八面体群的扭曲群代数和酷儿李超代数的对偶性”表示论纯数学组合方法的高级研究。

Manabu Yamaguchi: "A dualityof a twisted group algebra of the hyperoctahedral group and the queer Lie superalgebra"Advanced Studies in Pure Mathematics Combinatorial Methods in Representation Theory. 28. 401-422 (2000)

Manabu Yamaguchi：“超八面体群的扭曲群代数和酷儿李超代数的对偶性”表示论纯数学组合方法的高级研究。