中科院数学与系统科学研究院
数学研究所
学术报告
表示论研讨班
报告人： 胡泓昇 博士（北京大学）
题 目：Graphs and reflection representations（I）-- classifications and beyond
时 间：2023.09.14（星期四）14:30-15:30
地 点：数学院南楼N802
摘 要：A representation of a Coxeter group is called a reflection representation if each of the defining generators acts by an abstract reflection. In this talk, we classify the isomorphism classes of reflection representations (over the real or complex number field) using homology of certain graphs. The method can be used to obtain some surjections between Coxeter groups, and to construct some infinite dimensional irreducible representations of certain Coxeter groups.
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题 目：Graphs and reflection representations（II）-- exterior powers
时 间：2023.09.14（星期四）15:45-16:45
地 点：数学院南楼N802
摘 要：In 1968, R. Steinberg proved a theorem that if a Euclidean space is an irreducible representation of a reflection group in this space, then the exterior powers are pairwise non-isomorphic irreducible representations of the group. The proof relies on the inner product of the Euclidean space. In this talk, we extend this result to reflection representations in a more general context, where the inner product may not exist. Our proof contains some combinatorial methods on graphs.
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