On doubling construction for real unitary dual pairs

Takuya Konno, Kazuko Konno

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The Howe duality correspondence for a unitary dual pair over ℝ is usually formulated for the determinant cover of the dual pair. For applications to automorphic theory, one has to use the Weil representation of the unitary dual pair (not of the coverings) instead, which is constructed by the doubling argument of Harris et al (Theta dichotomy for unitary groups. J. Amer, Math. Soc. 9(4) (1996), 941-1004). In this paper, we calculate explicit formulae for the Fock model of this latter representation, and determine the Howe correspondence between K-types under this. This yields a description of the Howe duality correspondence between unitary groups in terms of certain ε-factors.

Original languageEnglish
Pages (from-to)35-85
Number of pages51
JournalKyushu Journal of Mathematics
Volume61
Issue number1
DOIs
Publication statusPublished - Jun 7 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On doubling construction for real unitary dual pairs'. Together they form a unique fingerprint.

  • Cite this