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Lie Groups and Representation Theory
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2015/04/14
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yuichiro Tanaka (Institute of Mathematics for Industry, Kyushu University)
Visible actions of compact Lie groups on complex spherical varieties (English)
Yuichiro Tanaka (Institute of Mathematics for Industry, Kyushu University)
Visible actions of compact Lie groups on complex spherical varieties (English)
[ Abstract ]
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).
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).
