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2020/10/16, 10/23 , 10/30, 11/06, 11/13 (5 weeks)10:00 ~ 11:50
2020/10/16, 10/23 , 10/30, 11/06, 11/13 (5 weeks)10:00 ~ 11:50
Speaker:
Chun-Ju Lai 賴俊儒助研究員 (AS)
Organizer:
Yung-Ning Peng 彭勇寧 (Department of Mathematics, National Central University )
Chih-Whi Chen 陳志瑋 (Department of Mathematics, National Central University )
Background and Purpose:
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.
Outline
Outline
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.
Watch the Course Video Here:
Watch the Course Video Here:
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