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One-Dimensional Representations of U (p,q) and the Howe Correspondence

✍ Scribed by Annegret Paul; Peter E. Trapa

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
349 KB
Volume
195
Category
Article
ISSN
0022-1236

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✦ Synopsis

We explicitly determine the theta lifts of all one-dimensional representations of Uðp; qÞ in terms of Langlands parameters, and determine exactly which lifts are unitary. Moreover, we show that such a lift is unitary if and only if it is a weakly fair derived functor module of the form A q ðlÞ: Finally, we show that the correspondence of unitary representations behaves well with respect to associated cycles.

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