Linear representations of twin cities
Walter Freyn

TL;DR
This paper extends the explicit flag complex descriptions from classical spherical and affine buildings to twin cities, providing linear representations as flag complexes of subspaces in Hilbert spaces, relevant for Kac-Moody groups.
Contribution
It generalizes the flag complex description to twin cities and constructs their linear representations in Hilbert spaces, advancing understanding of Kac-Moody geometric structures.
Findings
Explicit construction of twin city representations as flag complexes
Extension of classical building descriptions to twin cities
Framework for analyzing Kac-Moody group completions
Abstract
For spherical Tits buildings of the classical types there are well-known explicit descriptions as flag complexes. Similarly for affine buildings of the classical types there are explicit constructions in terms of lattices. In this article we generalize the flag complex description to twin cities, a generalization of twin buildings adapted to analytic completions of Kac-Moody groups as they appear for example in Kac-Moody geometry. We construct linear representations of twin cities as flag complexes of certain subspaces in Hilbert spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Algebra and Geometry · Advanced Operator Algebra Research
