2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Special lectures on advanced topics in Mathematics G
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ryosuke Kodera / Hironori Oya
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive (本館2階201数学系セミナー室)
- Class
- -
- Course Code
- MTH.E531
- Number of credits
- 200
- Course offered
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Course description:
This course is on the representation theory of Yangians and related integrable systems.
Aims:
Yangian is a class of algebras originated from the symmetry of solvable lattice models.
Their tensor product representations have intricate and rich structures with connections to Yang-Baxter equations and R-matrices.
Shifted Yangians, their variants, also have attracted interest recently.
We will introduce motivations of Yangians and their representation theory in the course.
We will also introduce recent developments of the study of shifted Yangians.
We will mainly give explanations of concrete examples that can be handled instead of detailed proofs.
Course description and aims
Understand the definition of Yangians and be familiar with calculation of their generators.
Be familiar with calculation of tensor product representations in some easy case.
Understand relationships between shifted Yangians and integrable systems.
Keywords
Yangian, Quantum group, Yang-Baxter equation, R-matrix, Representation theory, Integrable system
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Yang-Baxter equations and R-matrices Yangians: the RTT presentation and the Drinfeld presentation Tensor product representations Shifted Yangians | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required
Reference books, course materials, etc.
Will be announced in the class
References: https://www.math.s.chiba-u.ac.jp/~kodera/intensivelecture2023.html
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites
None required