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Lie Groups and Representation Theory
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2025/05/20
15:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Masatoshi KITAGAWA (Institute of Mathematics for Industry, Kyushu University)
On the restriction of good filtration in the branching problem of reductive Lie groups (Japanese)
Masatoshi KITAGAWA (Institute of Mathematics for Industry, Kyushu University)
On the restriction of good filtration in the branching problem of reductive Lie groups (Japanese)
[ Abstract ]
In arXiv:2405.10382, a Cartan subalgebra related to the branching problem of reductive Lie groups was defined. It is considered to control the size and shape of the continuous spectrum in irreducible decompositions, and is defined using the support of the action of the center of the universal enveloping algebra. Except in special cases, direct computations from the definition of this Cartan subalgebra are difficult.
In this talk, I will present results on restrictions of good filtrations and show a relation between the associated varieties of representations and the Cartan subalgebra.
I will also discuss applications to the necessary condition for discrete decomposability and related conjectures by T. Kobayashi.
In arXiv:2405.10382, a Cartan subalgebra related to the branching problem of reductive Lie groups was defined. It is considered to control the size and shape of the continuous spectrum in irreducible decompositions, and is defined using the support of the action of the center of the universal enveloping algebra. Except in special cases, direct computations from the definition of this Cartan subalgebra are difficult.
In this talk, I will present results on restrictions of good filtrations and show a relation between the associated varieties of representations and the Cartan subalgebra.
I will also discuss applications to the necessary condition for discrete decomposability and related conjectures by T. Kobayashi.
