Then we define
LECTURE 5. THE SYMPLECTIC CASE, PART II
1
!+,o = 1 -t'
! +,1=l+t,
l+t
!+,2 = 1 + t2'
f - (1 + t)(l - t^2 )
+,3 - 1 + t2 '
1
f-,k = -f.
+,k
Note that r ( C, m) is not always ± l.
139
This completes the definition of Gr. Another derivation of this invariant has
been given by Ionel and Parker [7].