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Naito Lab
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A lab that seeks to understand identities arising in mathematical physics and other areas through representations of quantum groups.
AboutAbout the lab
Understanding various identities through representation theory
The Naito Lab studies the representation theory of infinite-dimensional Lie algebras and quantum groups.
The lab aims to understand interesting identities arising in mathematical physics and other areas through representations of quantum groups.
Its main tools are crystal bases of quantum group representations and their concrete combinatorial realizations.
Key terms
- Identity
- An equation that holds for any values substituted for its variables
- Representation theory
- A field that studies abstract algebraic structures such as groups by translating them into concrete forms such as matrices
- Quantum group
- An algebra obtained by "deforming" a Lie algebra, which is an algebra expressing symmetry, through the introduction of a parameter
- Crystal basis
- A special basis of a quantum group representation. In the limit where the parameter approaches 0, it can be treated as a problem in combinatorics
ResearchResearch themes
*Illustrative imageQuantum K-theory of flag varieties
The lab studies the quantum K-theory ring, which expresses the counting of curves in algebraic terms, on spaces called flag varieties. It gives explicit presentations of this ring and determines its multiplication rules, such as the Chevalley formula.
*Illustrative imageConstructing representations with path models
The lab studies representations of quantum groups using models that describe them through the combinatorics of "paths," like polygonal lines in the plane. By extending this model, it constructs important polynomials such as Macdonald polynomials as counts of paths.
MembersFaculty
- ProfessorSatoshi NaitoPublications ↗
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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” Tom Ruen / Public domain (cropped)
- Quantum K-theory of flag varieties: “Bruhat order S^4” Odisub / CC BY-SA 4.0 (cropped)
- Constructing representations with path models: “Schroeder-Hipparcus paths 2x2” Giammarco Ferrari / CC BY-SA 4.0 (cropped)
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