Institute of Mathematics for Industry

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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

Place Seminar Room 1, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Toshihisa KUBO (Graduate School of Mathematical Sciences, the University of Tokyo)

summary:
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.