ON DOUBLING CONSTRUCTION FOR REAL UNITARY DUAL PAIRS
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概要
- 論文の詳細を見る
The Howe duality correspondence for a unitary dual pair over $ \mathbb{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 $ \mathbf{K} $-types under this. This yields a description of the Howe duality correspondence between unitary groups in terms of certain $ \varepsilon $-factors.
著者
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今野 和子
DEPT OF EDU., FUKUOKA UNIVERSITY OF EDUCATION
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今野 拓也
GRADUATE SCHOOL OF MATHEMATICS, KYUSHU UNIVERSITY
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KONNO Takuya
Graduate School of Mathematics Kyushu University
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Konno Kazuko
Department of Education Fukuoka University of Education
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