Part of the Applied Mathematical Sciences book series (AMS, volume 30)
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Let F1 and F2 be two polarizations of (X, ω) and V1 and V2 the representation spaces corresponding to F1 and F2 respectively. For strongly admissible pairs (F1, F2) of polarizations there is an intrinsically defined sesquilinear map K12:V1×V2→C, called the “Blattner-Kostant-Sternberg kernel.” The kernel K12 induces a linear map U12:V2→V1 such that V1 and σ2 ∈ V2 If U12 is unitary, the representation spaces V1 and V2 are said to be “unitarily related.”
KeywordsFibre Bundle Double Covering Positive Polarization Canonical Transformation Admissible Pair
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© Springer-Verlag New York Inc. 1980