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GEOMETRIC INVARIANTS FOR REPRESENTATIONS OF RESTRICTED LIE ALGEBRAS
Rolf Farnsteiner 教授(德国基尔大学)
2019-9-19 上午 09:00-10:00  闵行数学楼102报告厅

报告人简介:
Rolf Farnsteiner,现任德国基尔大学(Christian-Albrechts-Universit?t zu Kiel)教授。他1982年在汉堡大学获得博士学位。先后任美国Wisconsion大学(Milwaukee)教授,德国Bielefeld大学研究教授, 自2010年起担任德国基尔大学教授。 他是表示理论界重要数学家。研究领域与研究成果广泛。其中,在用代数表示理论方法研究Lie理论的表示及无穷小群概型的表示方面,独树一帜。
报告内容简介:Much of the progress in the representation theory of infinitesimal group schemes over the last thirty years has rested on methods related to cohomological support varieties and rank varieties. In this talk, we will focus on restricted Lie algebras, which correspond to infinitesimal groups of height 1. Motivated by Carlson’s seminal work on varieties for modular representations of finite groups, Friedlander-Parshall and Jantzen set forth a theory of module varieties for restricted Lie algebras in the mid-1980s. By introducing Jordan types of modules, their results were augmented and refined about 20 years later by Carlson, Friedlander, Pevtsova and Suslin. We will begin by reviewing the main aspects of this work along with stating some open problems. Let g be a restricted Lie algebra. Rank varieties and Jordan types seek to get information on a restricted g-module M by studying its restrictions M|e with respect the algebraic family of one-dimensional elementary abelian Lie algebras e ? g. In general, the collection E(d,g) of dimensional elementary abelian subalgebras of g is a closed subset of the Grassmannian Grd(g) of d-planes in g. It thus has the structure of a projective variety. In the second part of my talk, I will discuss more recent work that aims at understanding modules via restrictions larger subalgebras. This approach utilizes additional geometric invariants, which are obtained by associating morphisms and vector bundles to certain g-modules M. These invariants turn out to be determined by restrictions M|e to elementary abelian subalgebras e ∈E(d,g) of dimension d≥2.

主持人: 舒斌 教授
主办单位:数学科学学院 科技处