New preprint by Petra Schwer

The following is new on the ArXiv:

Chimney retractions in affine buildings encode orbits in affine flag varieties

Elizabeth Milićević, Petra Schwer, Anne Thomas

This paper determines the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provides 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 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 result generalizes the authors' previous joint work with Naqvi on groups over function fields.
Comments: 31 pages, 4 figures best viewed in color
Subjects: Group Theory (math.GR); Algebraic Geometry (math.AG); Combinatorics (math.CO); Representation Theory (math.RT)
MSC classes: 20E42 (Primary), 05E45, 14M15, 20G25, 51E24 (Secondary)
Cite as:

arXiv:2207.12923 [math.GR]

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Groups and topological groups

On Saturday 9 July, Olga Varghese will talk about "Automatic continuity" in the FU Berlin.

See you there!

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Equations in groups and complexity

On Tuesday 19 July, Olga Varghese will talk about her research in Newcastle.

See you there!

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Last Modification: 21.05.2021 - Contact Person: P. Schwer