Innovations in Incidence Geometry
- Innov. Incidence Geom.
- Volume 3, Number 1 (2006), 121-148.
The universal representation group of Huybrechts's dimensional dual hyperoval
A -dimensional dual hyperoval can be regarded as the image of a full -dimensional projective embedding of a dual circular space . The affine expansion of is a semibiplane and its universal cover is the expansion of the abstract hull of .
In this paper we consider Huybrechts’s dual hyperoval, namely where is the dual of the affine space and is induced by the embedding of the line grassmannian of in .
It is known that the universal cover of is a truncation of a Coxeter complex of type and that, if is the codomain of the abstract hull of , then is a subgroup of the Coxeter group of type , but is non-commutative. This information does not explain what the structure of is and how is placed inside . These questions will be answered in this paper.
Innov. Incidence Geom., Volume 3, Number 1 (2006), 121-148.
Received: 15 March 2006
Accepted: 22 May 2006
First available in Project Euclid: 28 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 15A75: Exterior algebra, Grassmann algebras 51E45 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]
Del Fra, Alberto; Pasini, Antonio. The universal representation group of Huybrechts's dimensional dual hyperoval. Innov. Incidence Geom. 3 (2006), no. 1, 121--148. doi:10.2140/iig.2006.3.121. https://projecteuclid.org/euclid.iig/1551323244