Infinite-dimensional flag varieties and other applications of well-ordered filtrationsAlgebra & Discrete Mathematics
|Nathaniel Gallup, UC Davis
|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.
Stay afterwards for a brief, informal reception. Refreshments will be self-provided.