Lie Groups and Representation Theory

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

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.

Graduate School of Mathematical Sciences, The University of Tokyo

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