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On conformally invariant systems of third order differential operators of Heisenberg type

Hold Date
2013-01-29 16:30〜2013-01-29 18:00
Seminar Room 1, Faculty of Mathematics building, Ito Campus
Object person
Toshihisa KUBO (Graduate School of Mathematical Sciences, the University of Tokyo)

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.