## 表現論セミナー Tensor products of Wallach representations and isotropy representations for singular unitary highest weight modules

2011年 　 7月 20日 15時 00分 ～ 2011年 　 7月 20日 16時 00分

We give an irreducible decomposition of some tensor products of Wallachrepresentations in terms of the isotropy representations for singular unitaryhighest weight modules. It is shown that the irreducible constituents are realizedon the vector bundles defined by the corresponding isotropy representations. This gives a Fock model version of some part of Dvorsky-Sahi's work on an extensionof the theta-correspondence.