Lie群論・表現論セミナー

開催情報 火曜日　16:30～18:00　数理科学研究科棟(駒場) 126号室 小林俊行 https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2015年04月14日(火)

16:30-18:00   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]
With the aim of uniform treatment of multiplicity-free representations of Lie groups, T. Kobayashi introduced the theory of visible actions on complex manifolds.

In this talk we consider visible actions of a compact real form U of a connected complex reductive algebraic group G on G-spherical varieties. Here a complex G-variety X is said to be spherical if a Borel subgroup of G has an open orbit on X. The sphericity implies the multiplicity-freeness property of the space of polynomials on X. Our main result gives an abstract proof for the visibility of U-actions. As a corollary, we obtain an alternative proof for the visibility of U-actions on linear multiplicity-free spaces, which was earlier proved by A. Sasaki (2009, 2011), and the visibility of U-actions on generalized flag varieties, earlier proved by Kobayashi (2007) and T- (2013, 2014).