LAB LOGA page on LabLog, a review site (not the lab's official page)
Oya Lab
Machine-translated · View original
The lab studies quantum groups and cluster algebras from the viewpoint of representation theory.
AboutAbout the lab
Exploring the representation theory of Lie algebras and quantum groups.
The Oya Lab studies representation theory in algebra, in particular Kac–Moody Lie algebras, quantum groups, and quantum cluster algebras.
As quantum groups, the lab works with quantum enveloping algebras and quantum coordinate rings.
In past graduation research, students have read books on Lie algebras and quantum groups, as well as books on Young diagrams, number theory, and combinatorial games.
The lab welcomes lab visits from students who wish to join it at the graduate level, and online visits are also possible.
Key terms
- Representation theory
- A field that studies the structure of abstract algebras such as groups and Lie algebras by translating them into matrix computations
- Quantum group
- An algebra obtained by deforming, with a parameter, an algebra that expresses symmetry, such as a Lie algebra
- Cluster algebra
- An algebra built by repeatedly exchanging sets of variables according to fixed rules
NewsLab news
Co-authored paper on quantum configuration spaces of decorated flags posted on arXiv
Co-authored paper on integral cluster structures on quantum coordinate rings posted on arXiv
Co-authored paper on polytopes and cluster structures of Schubert varieties published
Paper on cluster structures on coordinate rings of simple algebraic groups posted on arXiv
ResearchResearch themes
*Illustrative imageCluster Structures on Coordinate Rings of Quantum Groups
Hidden in the algebra known as the coordinate ring of a quantum group is a structure called a cluster algebra, in which generators are replaced step by step. The lab constructs this structure, including its integral version, and explores applications to representation theory.
*Illustrative imageQuantum Configuration Spaces of Flags
The lab quantizes the space of configurations of arranged objects called "decorated flags" and studies its algebraic properties. Using the ideas of cluster algebras, it clarifies what kind of algebra describes this space.
MembersFaculty
The members of the Oya Lab consist of faculty, and doctoral, master's, and undergraduate students.As of 2026
- Associate ProfessorHironori OyaPublications ↗
VoicesStudent voices
Ratings and reviews reflect the experiences of individual current or former students, not the lab's official views. Whether a lab has reviews, or how many, says nothing about the lab itself.
Students who take part in an interview may receive a thank-you gift worth ¥1,000, regardless of what they say.
Student ratings (0 students)
--
--
--
--
--
--
Student voices answer questions like these
- What's great about this lab?
- What did you learn after joining?
- What's the vibe, and what is the professor like?
- Who is this lab for?
- Where do graduates go?
Your experience can help younger students choose their lab. Your name won't be shown.
Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Oya Lab
Naito LabSchool of Science, Department of MathematicsRepresentation theory of infinite-dimensional Lie algebras a…
Yatagawa LabSchool of Science, Department of MathematicsAlgebraic number theory, étale cohomology, and ramification …
Gomi LabSchool of Science, Department of MathematicsAlgebraic topology
Purkait LabSchool of Science, Department of MathematicsNumber theory, automorphic forms, automorphic representation…The information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
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: “E8Petrie” Jgmoxness / CC BY-SA 3.0 (cropped)
- Cluster Structures on Coordinate Rings of Quantum Groups: “Polygon mouths and ears” Azylber / CC BY-SA 3.0 (cropped)
- Quantum Configuration Spaces of Flags: “Fano plane projective line symmetries scan” Jackson Walters / CC BY-SA 4.0 (cropped)
- Related lab (内藤研究室): “E8 edgeoverlap” Tom Ruen / Public domain (cropped)
- Related lab (谷田川研究室): “Riemann surface sqrt” Jan Homann / Public domain (cropped)
- Related lab (五味研究室): “Klein bottle glass2” PaulT (Gunther Tschuch) / CC BY-SA 4.0 (cropped)
- Related lab (プルカイト研究室): “J-inv-phase” Linas Vepstas / CC BY-SA 3.0 (cropped)
About LabLog
LabLog is a lab review app for students only. Student members at each university interview students in labs and publish what they say. Student voices can only be read by students who sign up with a university email address. Operated by bestiee Inc.
Learn more about LabLog ↗Search engines and AI may reference the basic lab info and rating summaries on this page and the description of LabLog. Student voices are for student members only. Automated collection by programs (scraping, or input to or training of AI) is prohibited under Article 8 of the Terms of Service. If you need data for research or analysis, please contact us.