[geometry-ml:06482] 東大数理・複素解析幾何セミナー 10/20

[shigeharu takayama]

皆様、

東大数理・複素解析幾何セミナーのお知らせです。

2025年10月20日(月) 10:30-12:00
数理科学研究科棟(駒場) 128号室
講演者：伊師 英之 氏 (大阪公立大学)
講演題目：A CR-Laplacian type operator for the Silov boundary of a
homogeneous Siegel domain (Japanese)
[ 講演概要 ]
Let $\Sigma$ be the Silov boundary of a homogeneous Siegel domain $D$
on which a Lie group $G$ acts transitively as affine transformations.
The CR-structure on $\Sigma$ naturally induced from the ambient
complex vector space is non-trivial if and only if $D$ is of non-tube
type. In this case, $\Sigma$ is naturally identified with a two-step
nilpotent Lie subgroup $N$ of $G$, called a generalized Heisenberg Lie
group. Since the CR-structure is invariant under the action of $G$,
the CR-cohomology space over $\Sigma$ can be regarded as a $G$-module.
We consider unitarization of this representation of $G$. The kernel of
the CR-Laplacian does not give the solution because the natural
Riemannian metric on $\Sigma$ is not $G$-invariant, so that the
$G$-action does not preserve the space of CR-harmonic forms.
Nevertheless, Nomura defined a unitary $G$-action on the space
indirectly when $G$ is split solvable. In this talk, we introduce a
space of  CR-cochains with $G$-invariant inner product defined via the
Fourier transform. Then the associated CR-operator is no longer a
differential operator, while the kernel of the operator gives a
unitarization of the representation of $G$ over the cohomology space.

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今後の予定はこちら
https://www.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

世話人
高山 茂晴、平地 健吾