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.