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Abe Lab
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The lab studies the representation theory of reductive algebraic groups, along with representations of Lie algebras and Hecke algebras.
AboutAbout the lab
Reading the shape of groups through representations.
Prof. Noriyuki Abe's lab studies representation theory.
At its core are representations of reductive algebraic groups and of the groups of their rational points.
The lab also studies representations of algebraic structures associated with these groups, such as Lie algebras and Hecke algebras.
Key terms
- Representation theory
- A field that studies abstract algebraic objects such as groups by expressing them concretely as matrices (linear transformations)
- Reductive algebraic group
- A general term for groups of matrices defined by equations that have good structural properties. The general linear group is a representative example
- Hecke algebra
- An algebra with a special multiplication rule that appears when studying representations of groups
ResearchResearch themes
The lab's field is representation theory, with the representation theory of reductive groups as its theme. It investigates representations of reductive algebraic groups, the groups of their rational points, and associated algebraic structures.
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MembersFaculty
- ProfessorNoriyuki AbePublications ↗
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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: “E8-with-thread” Jlrodri / CC BY-SA 3.0 (cropped)
- Representation Theory of Reductive Groups: “A3vzome” Mathphysman / CC BY-SA 4.0 (cropped)
- Related lab (Oshima Lab): “Weyl chambers for A2” Mathphysman / CC BY-SA 4.0 (cropped)
- Related lab (Iyama Lab): “Associaedre bleu” Kilom691 / CC BY-SA 4.0 (cropped)
- Related lab (Kezuka Lab): “Addition on cubic” Jean Brette / CC BY 3.0 (cropped)
- Related lab (Kobayashi Lab): “Hyperbolic tiling 7-2 7” Double sharp (talk), based on this picture by Jim McNeill, but with the centres of the heptagrams left uncoloured to prevent colours from overlapping. Created using Tyler and Paint. / Public domain (cropped)
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