作用素環と量子群

算子环和量子群

• 批准号: 14J02598
• 负责人: 荒野 悠輝
• 金额: $ 1.79万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2014
• 资助国家: 日本
• 起止时间: 2014-04-25 至 2017-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14J02598/
• 关键词: 量子群; テンソル圏; 性質(T); Howe-Moore性; 作用素環; q変形; KK理論; Drinfeld double

離散群上の正定値関数の研究は，幾何群論をはじめとして、作用素環，表現論，エルゴード理論など様々な研究において非常に重要な役割を果たしてきた．その量子群の類似として，De Commer-Freslon-Yamashitaによる離散量子群の中心的関数による近似性質/剛性，および等価な概念であるPopa-Vaes，Neshveyev-Yamashita，Ghosh-Jonesらによるテンソル圏の関数による近似性質/剛性は，部分因子環論との関連も含めて，重要な分野となってきた．私は，昨年度に引き続き，このような中心的近似性/剛性について調べた．特に，q-変形のDrinfeld doubleの表現論を推し進めることによって，私の以前の結果であるSUq(2n+1)の表現圏の性質(T)を拡張し，一般の高階の単純コンパクトLie群のq-変形の表現圏が性質(T)を持つことを示した．また，SUq(n)の場合には，より強く，中心的正定値関数(あるいは同じことであるが，その表現圏上の正定値関数)をSL(n,C)上の正定値関数を用いて表示することができた．また，正定値関数を拡張し，離散量子群上の中心的完全有界乗関数や，テンソル圏上の完全有界乗関数を調べた．このような中心的完全有界乗関数に関しては，De Commer-Freslon-YamashitaによるSUq(2)の中心的CMAPしか知られていなかったが，量子群の中心的Howe-Moore性および，テンソル圏のHowe-Moore性を導入し，q-変形についてこの性質を示した．これは中心的性質(T*)などの完全有界乗関数の剛性につながることが期待される．

It is very important to study the number of positive definite quantum groups on scattered groups, such as the number of positive definite quantum groups, the number of positive definite quantum groups on scattered groups, the number of positive definite quantum groups on scattered groups, the number of positive definite quantum groups on scattered groups, the number of positive definite quantum groups on scattered groups, the interaction factors, and so on. The concepts of quantum groups, such as the number, approximation, and Popa-Vaes,Neshveyev-Yamashita of the center of scattered quantum groups are very important. The number of Ghosh-Jones data is different. Some of the factors in the environment are related to the number of people who are similar to each other. Private, last year's information was introduced. The similarity of the center is very different. Special, Q-shaped Drinfeld double shows that you are improving your performance. In the past, the results showed that the SUq (2n+1) showed that there were significant differences between the two groups (T). In general, the number of positive determinants in the center was the same as that in the center. (t) in the past, SUq (n) showed that there was no difference between the two groups (T). The number of positive definite numbers on the SL (nmathC) shows that the number of positive definite numbers is completely bounded in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a discrete quantum group, the number of completely bounded numbers in the center of a discrete quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number of completely bounded numbers in the center of a scattered quantum group, the number The CMAP in the center of the De Commer-Freslon-Yamashita complex SUq (2), the Howe- Moore in the center of the quantum group, the Howe- in the center of the quantum group, the Howe-Moore in the center of the quantum group, the sex in the center of the quantum group, the Howe-Moore in the center of the quantum group, the number of characters in the center of the quantum group, the number of characters in the center of the quantum group, the number of properties in the center of the quantum group, the number of properties in the center of the quantum group.

项目成果

Diagrammatic method for representation theory of complex semisimple (quantum) groups

复杂半单（量子）群表示论的图解方法

• 发表时间: 2015
• 作者: 島田英明;島田英明;島田英明;Y. Arano;Yuki Arano;Yuki Arano;Y. Arano;Y. Arano;Y. Arano;Y. Arano;Yuki Arano;Yuki Arano
• 通讯作者: Yuki Arano

Irreducible spherical unitary representations of the Drinfeld double of SUq(3)

SUq(3) 的德林菲尔德双数的不可约球酉表示

• 发表时间: 2014
• 作者: 島田英明;島田英明;島田英明;Y. Arano;Yuki Arano;Yuki Arano;Y. Arano;Y. Arano;Y. Arano;Y. Arano;Yuki Arano;Yuki Arano;Yuki Arano;荒野悠輝;荒野悠輝
• 通讯作者: 荒野悠輝

Representation theory of Drinfeld doubles

德林菲尔德双打的表示论

• 发表时间: 2016
• 作者: 島田英明;島田英明;島田英明;Y. Arano;Yuki Arano;Yuki Arano;Y. Arano;Y. Arano;Y. Arano
• 通讯作者: Y. Arano

Unitary representations of Drinfeld doubles

德林菲尔德双打的酉表示

• 发表时间: 2016
• 作者: 島田英明;島田英明;島田英明;Y. Arano;Yuki Arano;Yuki Arano;Y. Arano
• 通讯作者: Y. Arano

Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups

德林菲尔德双数酉对偶与复半单李群的比较

• DOI: 10.1007/s00220-016-2704-x
• 发表时间: 2017
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: 島田英明;島田英明;島田英明;Y. Arano
• 通讯作者: Y. Arano