On doubling construction for real unitary dual pairs

Takuya Konno, Kazuko Konno

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)35-85
ページ数51
ジャーナルKyushu Journal of Mathematics
61
1
DOI
出版ステータス出版済み - 6 7 2007

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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