Cartan–Iwahori–Matsumoto decompositions for reductive groups

Reductive Groups

Representations of Reductive Groups

This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...

Pseudo-reductive Groups

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Reductive Groups over Fields

These are lecture notes that Tony Feng live-TEXed from a course given by Brian Conrad at Stanford in“winter” 2015, which Feng and Conrad edited afterwards. Two substitute lectures were delivered (by Akshay Venkatesh and Zhiwei Yun) when Conrad was out of town. This is a sequel to a previous course on the general structure of linear algebraic groups; some loose ends from that course (e.g., Cheva...

Conjugacy in Reductive Groups

Let G be a reductive algebraic group and H be a connected semisimple subgroup of G. The dimension data consists of the collection { dimV H } with V H denoting the space of points in V fixed by H , and where (ρ, V ) runs through all representations of G. One may ask if the dimension data determine H up to conjugacy or at least isomorphism. In other words, If H and H ′ have the same dimension dat...