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Sekiguchi Lab
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The lab studies the Penrose transform through the representation theory of Lie groups.
AboutAbout the lab
Capturing infinite-dimensional representations through integral transforms
Sekiguchi Lab studies the Penrose transform, which appears in mathematical physics, from the standpoint of the representation theory of semisimple Lie groups.
When infinite-dimensional representations of Lie groups are realized on spaces of functions, the more degenerate a representation is, the more differential equations it is thought to satisfy.
Just as the Radon transform is defined by integrating functions on a real manifold over submanifolds, a similar integral transform can be defined by integrating the cohomology of a complex manifold over cycles.
Using the geometric structure of homogeneous manifolds, the lab generalizes the Penrose transform to higher dimensions, aiming to describe singular infinite-dimensional unitary representations explicitly.
Key terms
- Lie group
- A group that collects together symmetries that vary smoothly and continuously, such as the set of all rotations
- Representation theory
- A field that studies abstract symmetries, such as those of groups, by expressing them concretely as matrices and linear transformations
- Radon transform
- A transform that converts a function into the collection of its integrals along lines, planes, and similar subspaces
ResearchResearch themes
The lab studies the Penrose transform, which appears in mathematical physics, from the standpoint of the representation theory of semisimple Lie groups. Using the geometric structure of homogeneous manifolds, it generalizes the Penrose transform to higher dimensions, aiming to describe singular infinite-dimensional unitary representations explicitly.
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MembersFaculty
- Associate ProfessorHideko Sekiguchi
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “HyperProjectionUsingRgl” Hou710 / CC BY-SA 4.0 (cropped)
- The Penrose Transform and Representation Theory: “Radon transform” Begemotv2718 at Russian Wikipedia / CC BY-SA 3.0 (cropped)
- Related lab (Bez Lab): “Fourieroperator equation visualization” Glogger / CC BY-SA 3.0 (cropped)
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- Related lab (Iwaki Lab): “AiryAi Abs Surface” Inductiveload / Public domain (cropped)
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