Bulletin of the Belgian Mathematical Society - Simon Stevin

Grassmannians of arbitrary rank

Simon Huggenberger

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Abstract

We introduce a generalization of Grassmannians of projective spaces that allows us to consider subspaces of any (possibly infinite) rank as points of the Grassmannian. We show that the spaces that we obtain, carry in a natural way the structure of a twin building.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 3 (2016), 321-343.

Dates
First available in Project Euclid: 6 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1473186508

Mathematical Reviews number (MathSciNet)
MR3545455

Zentralblatt MATH identifier
1353.14060

Subjects
Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 51A45: Incidence structures imbeddable into projective geometries 51E24: Buildings and the geometry of diagrams 51M35: Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]

Keywords
Twin buildings Grassmannians incidence geometry of infinite rank

Citation

Huggenberger, Simon. Grassmannians of arbitrary rank. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 3, 321--343. https://projecteuclid.org/euclid.bbms/1473186508


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