2019冬学期,水曜13:00-14:45: 幾何学XE / 数物先端科学III

四元数解析と表現論

Quaternionic analysis and representation theory.

I start with the interaction of representation theory of Lie groups with various branches of mathematics, and explain the fundamental role of reductive groups. I explained some classical formulas for quaternionic analysis as a generalization of complex analysis, and then explained “hidden symmetries” which are described in terms of infinite-dimensional representations of Lie groups and Lie algebras. Some of complicated formulas can be beautifully explained by representation-theoretic insight. For this, I also explained some general theory about how to understand sections for equivariant vector bundles.

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© Toshiyuki Kobayashi