Degenerate Principal Series
xin
is sufficient to check those where the Levi N is generated by A and one simple
reflection. Note that one must incorporate the reducibility of TAMP into these
computations.
The third condition reduces the problem to analyzing the reducibility of certain
induced representations of GL
2
(i r ) and Sp2(F) = S72(-^), where the results are
known.
As indicated, Theorem 3.1.2 is a generalization of the preceding arguments,
but it still requires a regularity condition. In the final chapter, we look explicitly at
degenerate principal series for Sp
4
(F) and Sp&(F), in general, modifying the kind
of arguments used in chapter 3 (including the definition of the graph for 7r) to allow
us to work out the non-regular case.
I would like to take this opportunity to thank some individuals who have
contributed to this paper, which is essentially my dissertation. First, I would like to
express my gratitude to Paul Sally Jr. for doing a fine job as advisor- it has been a
pleasure to work with him. This paper owes much to an idea of Marko Tadic, and I
would like to thank him for taking the time and effort to explain it to me. Finally, I
would like to thank Timothy Steger for carefully reading the first draft and making
many valuable suggestions, and the referee, for similar reasons.
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