Semi-ramified Quadrangles of Type E6, E7 and E8
Keyword(s):
This chapter deals with the case that the building at infinity of the Bruhat-Tits building Ξ is a Moufang semi-ramified quadrangle of type E⁶, E₇ and E₈. The basic proposition is that Ξ is a semi-ramified quadrangle if δΛ = 1 and δΨ = 2 holds. The chapter first considers the theorem supposing that ℓ = 6, that δΛ = 1 and δΨ = 2, and that the Moufang residues R0 and R1 are not both indifferent. This is followed by cases ℓ = 7 and ℓ = 8 as well as theorems concerning an anisotropic pseudo-quadratic space, a quaternion division algebra, standard involution, a proper involutory set, and isotropic and anisotropic quadratic spaces.
2009 ◽
Vol 61
(6)
◽
pp. 1325-1340
◽