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Lie Groups and Representation Theory
Seminar information archive ～04/28｜Next seminar｜Future seminars 04/29～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2023/06/06
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Atsumu Sasaki (Tokai University)
Visible actions on reductive spherical homogeneous spaces and their invariant measures
(Japanese)
Joint with Tuesday Seminar on Topology
Atsumu Sasaki (Tokai University)
Visible actions on reductive spherical homogeneous spaces and their invariant measures
(Japanese)
[ Abstract ]
Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property.
This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.
In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.
Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property.
This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.
In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.
