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Combinatorics and Representation Theory Lab
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The lab takes on counting problems at the intersection of combinatorics and representation theory.
AboutAbout the lab
Where combinatorics meets representation theory.
Prof. Okada studies the intersection of combinatorics and representation theory.
Combinatorics is the mathematics of discrete objects, and representation theory is the mathematics of studying how algebraic systems such as groups are realized as linear transformations.
The professor is interested in Young diagrams and symmetric functions related to the representation theory of classical groups, as well as counting problems for plane partitions and alternating sign matrices.
In the small-class master's courses, the topics listed include enumerative combinatorics, symmetric functions and their extensions, and quantum groups and crystal bases.
Key terms
- Representation theory
- Mathematics that studies the structure of algebraic systems such as groups by realizing them as matrices (linear transformations)
- Young diagram
- A combinatorial object made by arranging boxes. One with numbers written in the boxes is called a Young tableau
- Plane partition
- An object arising from combinatorics, also called a 3D Young diagram
- Alternating sign matrix
- A matrix whose entries are 0, 1, and −1 and which satisfies certain conditions
ResearchResearch themes
The lab works where combinatorics, representation theory, and other fields such as integrable systems meet. It approaches problems in representation theory with combinatorial methods and, conversely, tackles counting problems with ideas from representation theory and related fields.
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MembersFaculty
- ProfessorSoichi Okada
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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: “Line in combinatorics” Tensorproduct / CC BY-SA 4.0 (cropped)
- Combinatorial Representation Theory and Enumerative Combinatorics: “Schur functions rectangular example” Zajj Daugherty. / CC BY-SA 3.0 (cropped)
- Related lab (可換環論・環論・
表現論 （高橋 亮） ): “Tensor product of algebras” Jakob.scholbach / CC BY-SA 4.0 (cropped) - Related lab (表現論・
無限可積分系 （林 孝宏） ): “Dynkin diagram Dn” Rogilbert / Public domain (cropped) - Related lab (解析的整数論・代数的整数論
（ヘンリク・バッハマン） ): “ZetaFunction” Gaussianer / Public domain (cropped) - Related lab (代数幾何・
表現論・ 無限可積分系・数理物理 （柳田 伸太郎） ): “Truncated icosahedron cherry model by George W. Hart” George W. Hart / CC BY-SA 4.0 (cropped)
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