2020冬学期,水曜13:00-14:45: 数学続論XD / 数物先端科学IV

リー群の表現論の解析的手法 Lie Groups and Analytic Approach to Representation Theory

有限次元および無限次元における対称性を記述する表現の理論について、解析的なアイディアおよび幾何的な手法について基本的に重要な事柄を解説する。

Visible actions on complex manifolds and multiplicity-free representations (複素多様体上の可視的作用と無重複表現).

Multiplicity-free property of representations is an algebraic underlying structure of various expansion theorems in classical analysis. In the course, I begin with many examples of multiplicity-free representations, ranging from algebraic and combinatorial representation theory to classical analysis, and from finite-dimensional cases to infinite-dimensional cases with continuous spectrum. Then I explain a new approach to produce multiplicity-free representations systematically, namely, the theory of visible actions on complex manifolds and the propagation theorem of multiplicity-free property. This course is an outgrowth of my previous courses at Harvard University and at Tata Institute (for Ramanujan's 125 years anniversary).

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© Toshiyuki Kobayashi