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- Academic unit or major
- Mathematics
- Instructor(s)
- Oya Hironori
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive (数学系201セミナー室)
- Group
- -
- Course number
- ZUA.E341
- Credits
- 2
- Academic year
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- 2023/8/30
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
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.
Student learning outcomes
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 that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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 |
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
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None required
