## 保型形式の整数論月例セミナー

開催情報 土曜日　13:30～16:00　数理科学研究科棟(駒場) 123号室 織田 孝幸 https://www.ms.u-tokyo.ac.jp/~takayuki/monthly-seminar.html

### 2008年11月01日(土)

13:30-16:00   数理科学研究科棟(駒場) 123号室

$(\\mathfrka{g},K)$-module structure of the principal series of $GL(3,\\mathfrak{C})$
[ 講演概要 ]
We give explicit description of the action of $\\mathfrak{gl}(3,\\mathbf{C}$ to the whole space of $K$-finite vectors of a given principal series representation of $GL(3,\\mathbf{C})$.

Toward effectively computable integral basis of simple $\\mathbfrak{gl}_4$-modules of finite dimension. (II)
[ 講演概要 ]
This is a continuation of the talk at Osaka in the occation of Kanrei workshop of Prof. T. Ibukiyama.
We discuss a part of the injection $V_{\\lambda} \\rightarrow \\mathfrak{p} \\otimes V_{\\lambda}$. Here $V_{\\lambda}$ is a simple module with highest weight $\\lambda$, and $\\mathfrak{p}$ is the adjoint representation with highest weight $(1,0,0,-1)$.