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Lie群論・表現論セミナー
過去の記録 ～03/27｜次回の予定｜今後の予定 03/28～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2007年10月30日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
松本久義 氏 (東京大学大学院数理科学研究科)
On Weyl groups for parabolic subalgebras
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
松本久義 氏 (東京大学大学院数理科学研究科)
On Weyl groups for parabolic subalgebras
[ 講演概要 ]
Let ${\\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\\mathfrak p}$ of ${\\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\\mathfrak p}$
is conjugate to ${\\mathfrak p}$ under an inner automorphism of ${\\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
[ 参考URL ]Let ${\\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\\mathfrak p}$ of ${\\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\\mathfrak p}$
is conjugate to ${\\mathfrak p}$ under an inner automorphism of ${\\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
