Local theta correspondence of depth zero representations and theta dichotomy

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概要

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• 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 rep-resentations 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.

• 社団法人 日本数学会の論文
• 2002-10-01

著者

• Pan Shu-yen

  Department Of Mathematics National Cheng Kung University

関連論文

• Local theta correspondence of depth zero representations and theta dichotomy

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