一、課程背景與目的：

In representation theory, the Springer correspondence provides a geometric realization of the irreducible representations of Weyl groups via top cohomology of the Springer fibers, which are resolutions of nilpotent elements in Lie algebras. On the other hand, the universal enveloping algebras of Kac-Moody Lie algebras altogether with their irreducible integrable modules afford a geometric construction using Nakajima quiver varieties, which are geometric invariant theory (GIT) quotients of certain spaces of quiver representations.

Our goal is to explain the explicit realization of irreducible components of two-row Springer fibers in terms of Nakajima quiver varieties. Our treatment will be made accessible for graduate students and non-experts. For this purpose, we introduce along the way other central objects in representation theory.

二、課程之大綱與講者：

Week 1: Mini course on Springer fibers and quiver varieties - Lie algebras

For week 1 we give a crash course on the Lie algebras including the Schur duality and properties of the nilpotent orbits.

Week 2: Mini course on Springer fibers and quiver varieties - Symmetric groups

For week 2, we review the representation theory of the symmetric groups and their related combinatorics and geometry.

Week 3: Mini course on Springer fibers and quiver varieties - Springer fibers

In week 3 we will talk about the Springer correspondence as well as combinatorics related to irreducible components of two-row Springer fibers.

Week 4: Mini course on Springer fibers and quiver varieties - Quiver representations

Week 4 will be dedicated to basic properties of quiver representations.

Week 5: Mini course on Springer fibers and quiver varieties - Nakajima quiver varieties

In week 5 we explain how Springer fibers are realized as Nakajima quiver varieties.

三、課程詳細時間地點以及方式：

Week 1: 10/16 (Fr), 10:00 ~ 11:50, Room: To be determined.

Week 2: 10/23 (Fr), 10:00 ~ 11:50, Room: To be determined.

Week 3: 10/30 (Fr), 10:00 ~ 11:50, Room: To be determined.

Week 4: 11/06 (Fr), 10:00 ~ 11:50, Room: To be determined.

Week 5: 11/13 (Fr), 10:00 ~ 11:50, Room: To be determined.