A cohomological pairing of half-forms
HTML articles powered by AMS MathViewer
- by P. L. Robinson PDF
- 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, Lecture Notes in Math., vol. 836, Springer-Verlag, 1980, pp. 145-152. —, The Bargmann-Segal approach to symplectic spinors and half-forms for ${\text {M}}{{\text {P}}^c}$ structures, Warwick preprint, 1983. P. L. Robinson, ${\text {M}}{{\text {P}}^c}$ structures and applications, Warwick thesis, 1984. P. L. Robinson and J. H. Rawnsley, The metaplectic representation, ${\text {M}}{{\text {P}}^c}$ structures and geometric quantization (in preparation (1985)).
- 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
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 301 (1987), 251-261
- MSC: Primary 58F06; Secondary 17B10, 53C57
- DOI: https://doi.org/10.1090/S0002-9947-1987-0879572-7
- MathSciNet review: 879572