Monthly Seminar on Arithmetic of Automorphic Forms

Seminar information archive ~06/23Next seminarFuture seminars 06/24~

Date, time & place Saturday 13:30 - 16:00 123Room #123 (Graduate School of Math. Sci. Bldg.)

2008/11/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
宗野恵樹 (東京大学数理科学) 13:30-14:30
$(\\mathfrka{g},K)$-module structure of the principal series of $GL(3,\\mathfrak{C})$
[ Abstract ]
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 $GL(3,\\mathbf{C})$.
織田孝幸 (東京大学数理科学) 15:00-16:00
Toward effectively computable integral basis of simple $\\mathbfrak{gl}_4$-modules of finite dimension. (II)
[ Abstract ]
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 $(1,0,0,-1)$.