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Representations of GL_2 and p-adic Symmetric Spaces

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Let F be a finite field or a p-adic field. One method of constructing irreducible representations of G = GL_2(F), is to consider spaces on which G naturally acts and look at the representations arising from invariants of these spaces, such as cohomology groups. In this talk, I will discuss how this is done for abstract representations of G (when F is finite), and smooth representations of G (when F is p-adic). The first space is an affine algebraic variety, and the second a tower of rigid spaces. I will then mention some recent results about how this tower allows us to construct new interesting p-adic representations of G, before explaining how trying to adapt these methods leads naturally to considerations about certain geometric properties of these spaces.

This talk is part of the Junior Algebra and Number Theory seminar series.

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