2
Chris Jantzen
where
J =
In
\
J
(entries left vacant are zeros). Let K = Sp2n{0). This is a maximal compact
subgroup of Sp2n{F). It has a filtration of open compact normal subgroups
where
.. .K2Ii K,
Ki = {X e K\X = ImodV'}.
Let
A=\
a\
V
* » n
be a maximal split torus in Sp2n(F). Then, the Weyl group of Sp2n(F) is
W = NG(A)/A,
where NQ(A) denotes the normalizer of A in G. The Weyl group of Sp2n(F) has 2n-n!
elements and may be viewed as W = {permutations and sign changes of{ei,..., e
n
}}.
W is generated by the simple root reflections { s i , . . . , 5
n
}, where
/
\
1.
•1
si
1.
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