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October, 2002 Local theta correspondence of depth zero representations and theta dichotomy
Shu-Yen PAN
J. Math. Soc. Japan 54(4): 793-845 (October, 2002). DOI: 10.2969/jmsj/1191591993


In this paper, we prove that depth zero representations are preserved by local theta correspondence for any type I reductive dual pairs over a p-adic field. Moreover, the minimal K-types of the paired depth zero irreducible admissible representations are paired by the theta correspondence for finite reductive dual pairs. As a consequence, we prove that the Iwahori-spherical representations are preserved by the local theta correspondence. Then we obtain some partial result of theta dichotomy for finite reductive dual pairs and p-adic reductive dual pairs of symplectic and orthogonal group, which is analogous to S. Kudla and S. Rallis' result for p-adic unitary groups.


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Shu-Yen PAN. "Local theta correspondence of depth zero representations and theta dichotomy." J. Math. Soc. Japan 54 (4) 793 - 845, October, 2002.


Published: October, 2002
First available in Project Euclid: 5 October 2007

zbMATH: 1039.22012
MathSciNet: MR1921088
Digital Object Identifier: 10.2969/jmsj/1191591993

Primary: 11F27
Secondary: 20C33 , 22E50

Keywords: depth of a representation , local theta correspondence , minimal K-types , theta dichotomy

Rights: Copyright © 2002 Mathematical Society of Japan


Vol.54 • No. 4 • October, 2002
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