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

開催日時
2012年   12月 21日 16時 30分 ~ 2012年   12月 21日 18時 00分
場所
理学部3-307室
講演者
久保 利久氏 (東大数理)
 
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.

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