Date: July 8 (Mon) ~ July 10 (Wed), 2024

Venue: 129-406 (Seoul National University)

Invited Speakers:

Lecture Series I

Title:  Yangians and their representations (Alexander Molev)

Abstract: By the original definition of Drinfeld (1985), the Yangian Y(a) associated with a simple Lie algebra a is a canonical deformation of the universal enveloping algebra U(a[u]) in the class of Hopf algebras. The representation theory of the Yangians is a substantive and fascinating area which has since attracted significant interest from both mathematical physicists and representation theorists. In the lectures, we will discuss basic properties of the Yangians focusing on type A and will aim to prove the Drinfeld—Tarasov theorem classifying their finite-dimensional irreducible representations.

Lecture Series II

Title:  Basics on affine Yangians and their representations (Ryosuke Kodera)

Abstract: After recalling the Drinfeld realization of finite type Yangians, I will give the definition of the two-parameter affine Yangian of type A introduced by Guay. The most important thing is that this algebra admits coproduct and evaluation homomorphism, which are natural analogs of the corresponding properties of the Yangian of finite type A. Then I will explain a fundamental example of representations of the affine Yangian. It is the Fock space representation, which one defines by pulling back the level one integrable representation of the affine Lie algebra via the evaluation homomorphism. If time permits, I will discuss other methods to construct representations (Schur-Weyl type duality, geometric construction) and an expected relation to affine $W$-algebras.

Time table:

July 8th 

10:00am - 11:30am   Lecture I-1

2:00pm - 3:30pm         Lecture I-2

July 9th 

10:00am - 11:30am   Lecture I-3

 2:00pm - 3:30pm        Lecture II-1

July 10th 

10:00am - 11:30am   Lecture II-2

2:00pm - 3:30pm        Lecture II-3 

Organizing Committee: 

Jae-Hoon Kwon (Seoul National University)

Uhi Rinn Suh (Seoul National University)

Philsang Yoo (Seoul National University)

Support: 

NRF National Research Foundation of Korea

SNU Seoul National University

QSMS Center for Quantum Structures in Modules and Space