Lie Groups and Representation Theory

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

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2021/12/07

17:00-18:00   Room #on line (Graduate School of Math. Sci. Bldg.)
Toshihisa Kubo (Ryukoku University)
On the classification of the $K$-type formulas for the Heisenberg ultrahyperbolic equation (Japanese)
[ Abstract ]
About ten years ago, Kable constructed a one-parameter family $\square^{(n)}_s$ ($s\in \mathbb{C}$) of differential operators for $\mathfrak{sl}(n,\mathbb{C})$. He referred to $\square^{(n)}_s$ as the Heisenberg ultrahyperbolic operator. In the viewpoint of intertwining operators, $\square^{(n)}_s$ can be thought of as an intertwining differential operator between certain parabolically induced representations for $\widetilde{SL}(n,\mathbb{R})$. In this talk we discuss about the classification of the $K$-type formulas of the space of $K$-finite solutions to the differential equation $\square^{(3)}_sf=0$ for $\widetilde{SL}(3,\mathbb{R})$ and some related topics. This is joint work with Bent {\O}rsted.