| Title:
|
BGG sequences on spheres (English) |
| Author:
|
Somberg, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
509-527 |
| . |
| Category:
|
math |
| . |
| Summary:
|
BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called $K$-types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described. (English) |
| Keyword:
|
BGG sequences |
| Keyword:
|
invariant differential operators |
| Keyword:
|
branching rules |
| Keyword:
|
$K$-types |
| Keyword:
|
complexes |
| Keyword:
|
homogeneous spaces |
| MSC:
|
22E30 |
| MSC:
|
22E46 |
| MSC:
|
35P15 |
| MSC:
|
43A85 |
| idZBL:
|
Zbl 1037.43016 |
| idMR:
|
MR1795082 |
| . |
| Date available:
|
2009-01-08T19:04:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119186 |
| . |
| Reference:
|
[1] Baston R.J.: Almost Hermitean Symmetric Manifolds I. Local twistor theory.Duke Math. J. 63 1 (1991). MR 1106939 |
| Reference:
|
[2] Baston R.J.: Almost Hermitean Symmetric manifolds II. Differential invariants.Duke Math. J. . 63 1 (1991). MR 1106940 |
| Reference:
|
[3] Baston R.J., Eastwood M.G.: The Penrose Transform - its Interaction with Representation Theory.Oxford University Press, New York, 1989. Zbl 0726.58004, MR 1038279 |
| Reference:
|
[4] Bernstein I.N., Gelfand I.M., Gelfand S.I.: Structure of representations generated by vectors of highest weight.Funct. Anal. Appl. 5 (1971), 1-8. MR 0291204 |
| Reference:
|
[5] Branson T.: Stein-Weiss operators and ellipticity.J. Funct. Anal. 151 (1997), 334-383. Zbl 0904.58054, MR 1491546 |
| Reference:
|
[6] Branson T.: Spectra of self-gradients on spheres, preprint, University of Iowa, August 1998.. MR 1718236 |
| Reference:
|
[7] Branson T., Olafsson G., Ørsted B.: Spectrum generating operators and intertwining operators for representations induced from a maximal parabolic subgroup.J. Funct. Anal. 135 (1996), 163-205. MR 1367629 |
| Reference:
|
[8] Bureš J.: Special invariant operators I..ESI preprint 192 (1995). MR 1396170 |
| Reference:
|
[9] Čap A., Slovák J., Souček V.: Invariant operators with almost hermitean symmetric structures, III. Standard operators.to be published. |
| Reference:
|
[10] Čap A., Slovák J., Souček V.: Bernstein-Gelfand-Gelfand sequences.to be published. |
| Reference:
|
[11] Delanghe R., Souček V.: On the structure of spinor-valued differential forms.Complex Variables 18 (1992), 223-236. MR 1157930 |
| Reference:
|
[12] Eastwood M.G.: On the weights of conformally invariant operators.Twistor Newsl. 24 (1987), 20-23. |
| Reference:
|
[13] Eastwood M.G.: Notes on conformal differential geometry.Proc. of Winter School, Srní, in Suppl. Rend. Circ. Mat. di Palermo, ser. II, 43 (1996), 57-76. Zbl 0911.53020, MR 1463509 |
| Reference:
|
[14] Fegan H.D.: Conformally invariant first order differential operators.Quart. J. Math. 27 (1976), 371-378. Zbl 0334.58016, MR 0482879 |
| Reference:
|
[15] Fulton W.: Algebraic topology.Graduate Texts in Mathematics, Springer-Verlag, 1995. Zbl 0852.55001, MR 1343250 |
| Reference:
|
[16] Fulton W., Harris J.: Representation theory.Graduate texts in Mathematics 129, Springer-Verlag, 1991. Zbl 0744.22001, MR 1153249 |
| Reference:
|
[17] Jakobsen H.P.: Conformal invariants.Publ. RIMS, Kyoto Univ. 22 (1986), 345-361. MR 0849262 |
| Reference:
|
[18] Jakobsen H.P., Vergne M.: Wave and Dirac operators and representations of conformal group.J. Funct. Anal. 24 (1977), 52-106. MR 0439995 |
| Reference:
|
[19] Knapp A.: Lie Groups - Beyond an Introduction.Birkhäuser, 1996. Zbl 1075.22501, MR 1399083 |
| Reference:
|
[20] Knapp A.: Representation theory of semisimple groups, an overview based on examples.Princeton Mathematical Series 36, 1985. Zbl 0993.22001, MR 0855239 |
| Reference:
|
[21] Slovák J.: Natural operators on conformal manifolds.Dissertation Thesis, Brno, 1993. MR 1255551 |
| Reference:
|
[22] Souček V.: Conformal invariance of higher spin equations.in Proc. of Symp. `Analytical and Numerical Methods in Clifford Analysis', Lecture in Seifen, 1996. |
| Reference:
|
[23] Souček V.: Monogenic forms and the BGG resolution.preprint, Prague, 1998. MR 1845957 |
| Reference:
|
[24] Varadarajan V.S.: Harmonic Analysis on Semisimple Lie Groups.Cambridge University Press, 1986. Zbl 0924.22014 |
| Reference:
|
[25] Verma D.N.: Structure of certain induced representations of complex semisimple Lie algebras.Bull. Amer. Math. Soc. 74 (1968), 160-166. Zbl 0157.07604, MR 0218417 |
| Reference:
|
[26] Wünsch V.: On conformally invariant differential operators.Math. Nachr. 129 (1986), 269-281. MR 0864639 |
| . |
