 
Summary: Department of Mathematics & Statistics
Honours Seminar
Speaker: Chris Ramsey
Title: The Symplectic Group Relative to a Nondegenerate Sesquilinear Form
Date: October 19, 2006
Time: 2.30 pm
Location: College West 307.20
Abstract: Let H denote the division ring of quaternions and suppose that p and q are
nonnonegative integers and n D p C q. Consider the real vector space Kn
equipped with
the nondegenerate sesquilinear form OE ; W Kn
Kn
! K defined by
OE ; Á D 1Á1 C C pÁp pC1ÁpC1 nÁn :
The pseudosphere of Hn
is the manifold Sp;q .H/ D f 2 Kn
j OE ; D 1g, and the
isometry group of Hn
is the set Isop;q .H/ of all quaternionic matrices that leave the form
OE ; invariant. The group Ison;0 .H/ is the classical symplectic group Sp.n/ and Sn;0.H/
