Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
ON DOUBLING CONSTRUCTION FOR REAL UNITARY DUAL PAIRS
Takuya KONNOKazuko KONNO
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2007 Volume 61 Issue 1 Pages 35-82

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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.

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© 2007 by Faculty of Mathematics, Kyushu University
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