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Infinite-dimensional flag varieties and other applications of well-ordered filtrations

Algebra & Discrete Mathematics

Speaker: Nathaniel Gallup, UC Davis
Location: Zoom lecture
Start time: Thu, Oct 22 2020, 10:00AM

Subspace filtrations of infinite-dimensional vector spaces behave differently from their finite-dimensional counterparts in a very important way: not every infinite filtration has an adapted basis. This fact causes many interesting difficulties (in the representation theory of infinite quivers for example), but can be fixed by adding a well-ordered hypothesis which allows the use of transfinite induction. We'll use this idea to define an infinite-dimensional full flag variety, and to prove a Bruhat-like decomposition for it. In an effort to take the closure of an infinite Schubert cell, we'll use the "functor of points" approach to extend our definition of the infinite-dimensional flag variety, and discuss various properties (representability, descent, etc.) of the resulting presheaf on the category of schemes.

All meetings this quarter will be by Zoom. Please see announcements or contact organizers for the passcode. Slides for the talk are also available.

Stay afterwards for a brief, informal reception. Refreshments will be self-provided.