Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Summary:
Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.
References:
[1] Baston R.: Quaternionic complexes. J. Geom. Phys. 8 (1992), 29–52. MR 1165872 | Zbl 0764.53022
[2] Baston R. J., Eastwood M. G.: Penrose transform; Its interaction with representation theory. Clarendon Press, Oxford, 1989. MR 1038279 | Zbl 0726.58004
[3] Calderbank D. M. J., Diemer T.: Differential invariants and curved Bernstein–Gelfand–Gelfand sequences. J. Reine angew. Math. 537 (2001), 67–103. MR 1856258 | Zbl 0985.58002
[4] Čap A.: Two constructions with parabolic geometries. preprint, arXiv:math.DG/0504389 MR 2287124 | Zbl 1120.53013
[5] Čap A., Schichl H.: Parabolic geometries and canonical Cartan connections. Hokkaido Math. J. 29 3 (2000), 453–505. MR 1795487 | Zbl 0996.53023
[6] Čap A., Slovák J., Souček V.: Bernstein-Gelfand-Gelfand sequences. Ann. of Math. (2) 154 1 (2001), 97–113. MR 1847589
[7] Colombo F., Sabadini A., Sommen F., Struppa D.: Analysis of Dirac systems and computational algebra. Birkhäuser, Basel, 2004. MR 2089988 | Zbl 1064.30049
[8] Franek P.: Generalized Verma module homomorphisms in singular character. submitted to Proc. of the Winter School ’Geometry and Physics’, Srni, 2006. MR 2322409 | Zbl 1164.22310
[9] Krump L.: Construction of BGG sequences for AHS structures. Comment. Math. Univ. Carolin. 42 1 (2001), 31–52, MR 1825371 | Zbl 1054.53071
[10] Krump L., Souček V.: Hasse diagrams for parabolic geometries. Proc. of ’The 22nd Winter School ’Geometry and Physics’, Srní 2002, Rend. Circ. Mat. Palermo (2) Suppl. 71 (2003). MR 1982440 | Zbl 1047.53014
[11] Nacinovich M.: Complex analysis and complexes of differential operators. LNM 950, Springer-Verlag, Berlin, 1980. MR 0672785
[12] Sharpe R. W.: Differential geometry. Grad. Texts in Math. 166 (1997). MR 1453120 | Zbl 0876.53001
[13] Slovák J.: Parabolic geometries. Research Lecture Notes, Part of DrSc. Dissertation, Preprint IGA 11/97, electronically available at www.maths.adelaide.edu.au.
[14] Šmíd D.: The BGG diagram for contact orthogonal geometry of even dimension. Acta Univ. Carolin. Math. Phys. 45 (2004), 79–96. MR 2109696 | Zbl 1138.17310
Search
Partner of
