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.
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.
Yangian, Quantum group, Yang-Baxter equation, R-matrix, Representation theory, Integrable system
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
This is a standard lecture course.
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. |
None required.
Will be announced in the class.
References: https://www.math.s.chiba-u.ac.jp/~kodera/intensivelecture2023.html
Assignments (100%).
None required.