Lie Groups and Representation Theory

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Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2022/04/19

17:30-18:30   Room #online (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Toshihisa Kubo (Ryukoku University)
On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces
(Japanese)
[ Abstract ]
Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a \emph{differential symmetry breaking operator} (differential SBO for short)
([T. Kobayashi, Differential Geom. Appl. (2014)]).

In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard
Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$.
In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.