分野別セミナー

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