ON DOUBLING CONSTRUCTION FOR REAL UNITARY DUAL PAIRS

• KONNO Takuya

  Graduate School of Mathematics Kyushu University

• KONNO Kazuko

  Department of Education Fukuoka University of Education

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.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 61 (1), 35-82, 2007

  九州大学大学院数理学研究院

キーワード

• reductive dual pair
• Weil representation
• Howe duality

詳細情報

• CRID: 1390001205229699072
• NII論文ID: 130000063183
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.61.35
• ISSN: 18832032
• ISSN: 13406116
• MRID: 2317282
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/61/1/61_1_35/_pdf
• 本文言語コード: en
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