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Keywords:
BGG sequences; invariant differential operators; branching rules; $K$-types; complexes; homogeneous spaces
BGG sequences; invariant differential operators; branching rules; $K$-types; complexes; homogeneous spaces
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.
References:
[1] Baston R.J.: Almost Hermitean Symmetric Manifolds I. Local twistor theory. Duke Math. J. 63 1 (1991). MR 1106939
[2] Baston R.J.: Almost Hermitean Symmetric manifolds II. Differential invariants. Duke Math. J. . 63 1 (1991). MR 1106940
[3] Baston R.J., Eastwood M.G.: The Penrose Transform - its Interaction with Representation Theory. Oxford University Press, New York, 1989. MR 1038279 | Zbl 0726.58004
[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
[5] Branson T.: Stein-Weiss operators and ellipticity. J. Funct. Anal. 151 (1997), 334-383. MR 1491546 | Zbl 0904.58054
[6] Branson T.: Spectra of self-gradients on spheres, preprint, University of Iowa, August 1998. MR 1718236
[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
[8] Bureš J.: Special invariant operators I. ESI preprint 192 (1995). MR 1396170
[9] Čap A., Slovák J., Souček V.: Invariant operators with almost hermitean symmetric structures, III. Standard operators. to be published.
[10] Čap A., Slovák J., Souček V.: Bernstein-Gelfand-Gelfand sequences. to be published.
[11] Delanghe R., Souček V.: On the structure of spinor-valued differential forms. Complex Variables 18 (1992), 223-236. MR 1157930
[12] Eastwood M.G.: On the weights of conformally invariant operators. Twistor Newsl. 24 (1987), 20-23.
[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. MR 1463509 | Zbl 0911.53020
[14] Fegan H.D.: Conformally invariant first order differential operators. Quart. J. Math. 27 (1976), 371-378. MR 0482879 | Zbl 0334.58016
[15] Fulton W.: Algebraic topology. Graduate Texts in Mathematics, Springer-Verlag, 1995. MR 1343250 | Zbl 0852.55001
[16] Fulton W., Harris J.: Representation theory. Graduate texts in Mathematics 129, Springer-Verlag, 1991. MR 1153249 | Zbl 0744.22001
[17] Jakobsen H.P.: Conformal invariants. Publ. RIMS, Kyoto Univ. 22 (1986), 345-361. MR 0849262
[18] Jakobsen H.P., Vergne M.: Wave and Dirac operators and representations of conformal group. J. Funct. Anal. 24 (1977), 52-106. MR 0439995
[19] Knapp A.: Lie Groups - Beyond an Introduction. Birkhäuser, 1996. MR 1399083 | Zbl 1075.22501
[20] Knapp A.: Representation theory of semisimple groups, an overview based on examples. Princeton Mathematical Series 36, 1985. MR 0855239 | Zbl 0993.22001
[21] Slovák J.: Natural operators on conformal manifolds. Dissertation Thesis, Brno, 1993. MR 1255551
[22] Souček V.: Conformal invariance of higher spin equations. in Proc. of Symp. `Analytical and Numerical Methods in Clifford Analysis', Lecture in Seifen, 1996.
[23] Souček V.: Monogenic forms and the BGG resolution. preprint, Prague, 1998. MR 1845957
[24] Varadarajan V.S.: Harmonic Analysis on Semisimple Lie Groups. Cambridge University Press, 1986. Zbl 0924.22014
[25] Verma D.N.: Structure of certain induced representations of complex semisimple Lie algebras. Bull. Amer. Math. Soc. 74 (1968), 160-166. MR 0218417 | Zbl 0157.07604
[26] Wünsch V.: On conformally invariant differential operators. Math. Nachr. 129 (1986), 269-281. MR 0864639
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