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Algebra 1 Lab (Representation Theory, Algebraic Analysis and Mathematical Physics; Syu Kato)
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A lab that realizes representations of algebraic systems using tools from geometry.
AboutAbout the lab
Studying how symmetry appears, through geometric objects.
The Syu Kato Lab studies geometric representation theory.
It realizes representations of algebraic systems arising from semisimple Lie algebras and their root systems (Hecke algebras, quantum groups, algebraic groups, and others), mainly by using geometric structures.
The lab investigates the classification of irreducible and unitary representations and the structure of categories of representations.
By comparing different realizations, it also studies integrable systems, orthogonal function systems, and number-theoretic invariants.
Key terms
- Representation theory
- The field that, given a symmetry (an algebraic system), classifies the ways it can appear (its representations) and constructs them concretely.
- Quantum group
- An algebraic system obtained by deforming the symmetry of a Lie algebra or similar object with a parameter.
- Irreducible representation
- The basic unit of representations: one that cannot be broken down into smaller representations.
ResearchResearch themes
The lab conducts research in geometric representation theory. It realizes representations of algebraic systems using geometric objects and studies their properties.
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MembersFaculty
- ProfessorSyu Kato
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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 edgeoverlap-eight” Tom Ruen (talk) / Public domain (cropped)
- Realizing representations of algebraic systems geometrically: “Affine Dynkin diagrams” self / Public domain (cropped)
- Related lab (Algebra 1 (Number Theory, Representation Theory) Lab (Miyu Suzuki)): “Cayley graphs of quaternion group” PSL27 / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 2 (Algebraic Geometry) Lab): “Clebsch Cubic” Fly by Night / CC BY-SA 3.0 (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Kaoru Hiraga)): “KleinjCont” Empetrisor / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Ito)): “EllipticGroup” Thomas Cooper / Public domain (cropped)
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