Construction of BGG sequences for AHS structures
Krump, Lukáš
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 31-52 / Harvested from Czech Digital Mathematics Library

This paper gives a description of a method of direct construction of the BGG sequences of invariant operators on manifolds with AHS structures on the base of representation theoretical data of the Lie algebra defining the AHS structure. Several examples of the method are shown.

Publié le : 2001-01-01
Classification:  17B10,  22E46,  43A85,  53A55,  53C30
@article{119222,
     author = {Luk\'a\v s Krump},
     title = {Construction of BGG sequences for AHS structures},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {31-52},
     zbl = {1054.53071},
     mrnumber = {1825371},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119222}
}
Krump, Lukáš. Construction of BGG sequences for AHS structures. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 31-52. http://gdmltest.u-ga.fr/item/119222/

Baston R.J. Almost Hermitian symmetric manifolds, I: Local twistor theory, II: Differential invariants, Duke Math. J. 63 (1991), 81-111, 113-138. (1991) | MR 1106939

Baston R.J.; Eastwood M.G. Penrose Transform; Its Interaction with Representation Theory, Clarendon Press, Oxford, 1989. | MR 1038279 | Zbl 0726.58004

Bernstein I.N.; Gelfand I.M.; Gelfand S.I. Structure of representations generated vectors of highest weight, Funct. Anal. Appl. 5 (1971), 1-8. (1971) | MR 0291204

Bernstein I.N.; Gelfand I.M.; Gelfand S.I. Differential operators on the base affine space and a study of $\frak g$-modules, in ``Lie Groups and their Representations'' (ed. I.M. Gelfand) Adam Hilger, 1975, pp.21-64. | MR 0578996

Branson T.; Ólafsson G.; Ørsted B. Spectrum generating operators and intertwining operators for representations induced from a maximal parabolic subgroup, J. Funct. Anal. 135 (1996), 163-205. (1996) | MR 1367629

Bureš J. Special invariant operators I, Comment. Math. Univ. Carolinae 37.1 (1996), 179-198. (1996) | MR 1396170

Čap A. Translation of natural operators on manifolds with AHS-structures, Archivum Math. (Brno) 32.4 (1996), 249-266, electronically available at www.emis.de. (1996) | MR 1441397

Čap A.; Schichl H. Parabolic Geometries and Canonical Cartan Connections, preprint ESI 450, electronically available at www.esi.ac.at. | MR 1795487

Čap A.; Slovák J.; Souček V. Invariant operators on manifolds with almost Hermitian symmetric structures, I. Invariant differentiation, Acta Math. Univ. Commenianae 66 (1997), 33-69, electronically available at www.emis.de. (1997) | MR 1474550

Čap A.; Slovák J.; Souček V. Invariant operators on manifolds with almost Hermitian symmetric structures, II. Normal Cartan connections, Acta Math. Univ. Commenianae, 66 (1997), 203-220, electronically available at www.emis.de. (1997) | MR 1620484

Čap, A.; Slovák J.; Souček V. Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard Operators, ESI Preprint 613, to appear in J. Differential Geom. Appl., electronically available at www.esi.ac.at. | MR 1757020 | Zbl 0969.53004

Eastwood M.G. On the weights of conformally invariant operators, Twistor Newsl. 24 (1987), 20-23. (1987)

Eastwood M.G.; Slovák J. Semi-holonomic Verma modules, J. Algebra 197 (1997), 424-448. (1997) | MR 1483772

Fegan H.D. Conformally invariant first order differential operators, Quart. J. Math. 27 (1976), 371-378. (1976) | MR 0482879 | Zbl 0334.58016

Fulton W.; Harris J. Representation Theory - A First Course, Springer-Verlag (GTM), 1991. | MR 1153249 | Zbl 0744.22001

Garland H.; Lepowsky J. Lie Algebra Homology and the Macdonald-Kac Formulae, Inv. Math. 34, Springer, 1976. | MR 0414645

Gindikin S.G. Generalized conformal structures, Twistors in Mathematics and Physics, LMS Lecture Notes 156, Cambridge Univ. Press, 1990, pp.36-52. | MR 1089908 | Zbl 0788.22008

Goncharov A.B. Generalized conformal structures on manifolds, Selecta Math. Soviet. 6 (1987), 308-340. (1987) | MR 0925263 | Zbl 0632.53038

Humphreys J.E. Introduction to Lie Algebras and Representation Theory, Springer-Verlag, 1972. | MR 0323842 | Zbl 0447.17002

Jakobsen H.P. Conformal invariants, Publ. RIMS, Kyoto Univ. 22 (1986), 345-361. (1986) | MR 0849262

Jacobson N. Lie Algebras, Interscience Tracts, No. 10, 1962. | MR 0143793 | Zbl 0333.17009

Johnson K.D. Decomposition of Exterior Algebras, Contemp. Math. 191, AMS, 1995. | MR 1365537 | Zbl 0851.57040

Kobayashi S.; Nagano T. On filtered Lie algebras and geometric structures I, J. Math. Mech. 13 (1964), 875-907. (1964) | MR 0168704 | Zbl 0142.19504

Kolář I.; Michor P.W.; Slovák J. Natural Operations in Differential Geometry, Springer, 1993. | MR 1202431

Lepowsky J. A generalization of the Bernstein-Gelfand-Gelfand resolution, J. Algebra 49 (1977), 496-511. (1977) | MR 0476813 | Zbl 0381.17006

Sharpe R.W. Differential Geometry, Graduate Texts in Mathematics 166, Springer-Verlag, 1997. | MR 1453120 | Zbl 0876.53001

Slovák J. On the geometry of almost Hermitian symmetric structures, in Proceedings of the Conference Differential Geometry and Applications, 1995, Brno, Masaryk University, Brno (1996), pp.191-206, electronically available at www.emis.de. | MR 1406338

Slovák J. Parabolic geometries, Research Lecture Notes, Part of DrSc. Dissertation, Preprint IGA 11/97, electronically available at www.maths.adelaide.edu.au.

Verma D.N. Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968), 160-166. (1968) | MR 0218417 | Zbl 0157.07604

Wünsch V. On conformally invariant differential operators, Math. Nachr. 129 (1986), 269-281. (1986) | MR 0864639