A cohomological pairing of half-forms

Robinson, P. L.

doi:10.1090/S0002-9947-1987-0879572-7

A cohomological pairing of half-forms
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Trans. Amer. Math. Soc. 301 (1987), 251-261 Request permission

Abstract:

Blattner and Rawnsley have constructed half-forms for regular polarizations of arbitrary index. We show how to pair these half-forms into a line bundle fashioned purely from the symplectic data, with no assumption on the intersection of the polarizations. Our pairing agrees with the regular BKS pairing when the polarizations are positive.

References

Robert J. Blattner, The metalinear geometry of non-real polarizations, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Lecture Notes in Math., Vol. 570, Springer, Berlin, 1977, pp. 11–45. MR 0451296
Robert J. Blattner and John H. Rawnsley, Quantization of the action of $\textrm {U}(k,\,l)$ on $\textbf {R}^{2(k+l)}$, J. Funct. Anal. 50 (1983), no. 2, 188–214. MR 693228, DOI 10.1016/0022-1236(83)90067-8
Bertram Kostant, Symplectic spinors, Symposia Mathematica, Vol. XIV (Convegno di Geometria Simplettica e Fisica Matematica, INDAM, Rome, 1973) Academic Press, London, 1974, pp. 139–152. MR 0400304
J. H. Rawnsley, On the pairing of polarizations, Comm. Math. Phys. 58 (1978), no. 1, 1–8. MR 468930

Non-positive polarizations and half-forms

The Bargmann-Segal approach to symplectic spinors and half-forms for

structures

structures and applications

The metaplectic representation

structures and geometric quantization

André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
Joseph A. Wolf, The action of a real semisimple group on a complex flag manifold. I. Orbit structure and holomorphic arc components, Bull. Amer. Math. Soc. 75 (1969), 1121–1237. MR 251246, DOI 10.1090/S0002-9904-1969-12359-1