## 幾何学コロキウム　Visible actions of compact Lie groups on complex spherical varieties

2016年 　 11月 25日 16時 30分 ～ 　 18時 00分

3号館204室

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 spherical varieties. Here a connected 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.
We show the visibility of U-actions on spherical varieties
by using the method of induction of visible actions.
The method of induction of visible actions was introduced by Kobayashi
(2005) for the case of complex spherical nilpotent orbits of type A,
and recently extended by A. Sasaki (2016) to the case of complex
spherical nilpotent orbits of arbitrary type.
Our proof is highly motivated by those earlier results.

<注意>

（１１月１６日以前では，　講演日が１２月２５日となっていました．　１１月２５日が正しいです）．