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University of Sydney Algebra Seminar

Anne Thomas

Friday 19 August, 12-1pm, Place: Carslaw 173

Chimney retractions in affine buildings encode orbits in affine flag varieties

We determine the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provide a unified framework to study orbits in affine flag varieties. We introduce the notion of labeled folded galleries for any affine building X and use these to describe the images and preimages of chimney retractions. When X is the building for a group with an affine Tits system, such as the Bruhat-Tits building for a group over a local field, we can then relate labeled folded galleries and shadows to double coset intersections in affine flag varieties. This is joint work with Elizabeth Mili\'cevi\'c and Petra Schwer.