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Lie群論・表現論セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2019年10月30日(水)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Quentin Labriet 氏 (Reims University)
On holographic transform (English)
Quentin Labriet 氏 (Reims University)
On holographic transform (English)
[ 講演概要 ]
In representation theory, decomposing the restriction of a given representation $¥pi$ of a Lie group $G$ to an appropriate subgroup $G'$ is an important issue referred to as a branching law. In this context,one can define symmetry breaking operators, as $G'$-intertwining operators between the restriction $¥pi¥vert_{G'}$ and its irreducible components. Going in the opposite direction gives rise to holographic operators and the notion of holographic transform.
I will illustrate this construction by two examples :
- the diagonal case where one considers the restriction problem for $¥pi$ being an outer product of two holomorphic discrete series representations, $G=SL(2,R)¥times SL(2,R)$ and $G'=SL(2,R)$.
- the conformal case for the restriction of a scalar valued holomorphic discrete series representation $¥pi$ of $G=SO(2,n)$ to $G'=SO(2,n-1)$.
I will then explain different methods for an explicit construction of such holographic operators in these cases, and present some of my results and open problems in this direction.
In representation theory, decomposing the restriction of a given representation $¥pi$ of a Lie group $G$ to an appropriate subgroup $G'$ is an important issue referred to as a branching law. In this context,one can define symmetry breaking operators, as $G'$-intertwining operators between the restriction $¥pi¥vert_{G'}$ and its irreducible components. Going in the opposite direction gives rise to holographic operators and the notion of holographic transform.
I will illustrate this construction by two examples :
- the diagonal case where one considers the restriction problem for $¥pi$ being an outer product of two holomorphic discrete series representations, $G=SL(2,R)¥times SL(2,R)$ and $G'=SL(2,R)$.
- the conformal case for the restriction of a scalar valued holomorphic discrete series representation $¥pi$ of $G=SO(2,n)$ to $G'=SO(2,n-1)$.
I will then explain different methods for an explicit construction of such holographic operators in these cases, and present some of my results and open problems in this direction.
