## 表現論セミナー On conformally invariant systems of third order differential operators of Heisenberg type

2012年 　 12月 21日 16時 30分 ～ 2012年 　 12月 21日 18時 00分

Conformally invariant systems are systemsof differential operators, which are equivariant under anaction of a Lie algebra. Recently, Barchini, Kable, andZierau have constructed a number of examples of such systemsof operators. The construction was systematic, but theexistence of such a system of third order operators wasleft open in two cases, namely, for $\frak{sl}(3,\mathbb{C})$ and $\frak{so}(8,\mathbb{C})$.In this talk we show that thethird order systems do exist for both cases. We then presentin detail a construction of such a system of operators for $\frak{sl}(3, \mathbb{C})$. The generalized Verma moduleassociated with the third order systems plays a key role.