Spectrum generating on twistor bundle
Branson, Thomas ; Hong, Doojin
Archivum Mathematicum, Tome 042 (2006), p. 169-183 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

Spectrum generating technique introduced by Ólafsson, Ørsted, and one of the authors in the paper (Branson, T., Ólafsson, G. and Ørsted, B., Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroups, J. Funct. Anal. 135 (1996), 163–205.) provides an efficient way to construct certain intertwinors when $K$-types are of multiplicity at most one. Intertwinors on the twistor bundle over $S^1\times S^{n-1}$ have some $K$-types of multiplicity 2. With some additional calculation along with the spectrum generating technique, we give explicit formulas for these intertwinors of all orders.

Publié le : 2006-01-01
Classification:  22E46,  53C28 
@article{108025,
     author = {Thomas Branson and Doojin Hong},
     title = {Spectrum generating on twistor bundle},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {169-183},
     zbl = {1164.53358},
     mrnumber = {2322405},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108025}
}

Branson, Thomas; Hong, Doojin. Spectrum generating on twistor bundle. Archivum Mathematicum, Tome 042 (2006) pp. 169-183. http://gdmltest.u-ga.fr/item/108025/

Branson T. Group representations arising from Lorentz conformal geometry, J. Funct. Anal. 74 (1987), 199–291. (1987) | MR 0904819 | Zbl 0643.58036

Branson T. Nonlinear phenomena in the spectral theory of geometric linear differential operators, Proc. Symp. Pure Math. 59 (1996), 27–65. (1996) | MR 1392983 | Zbl 0857.58042

Branson T. Stein-Weiss operators and ellipticity, J. Funct. Anal. 151 (1997), 334–383. (1997) | MR 1491546 | Zbl 0904.58054

Branson T. Spectra of self-gradients on spheres, J. Lie Theory 9 (1999), 491–506. (1999) | MR 1718236 | Zbl 1012.22026

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

Hong D. Eigenvalues of Dirac and Rarita-Schwinger operators, Clifford Algebras and their Applications in Mathematical Physics, Birkhäuser, 2000. | MR 2025981 | Zbl 1080.53044

Hong D. Spectra of higher spin operators, Ph.D. Dissertation, University of Iowa, 2004. | MR 2706219

Kosmann Y. Dérivées de Lie des spineurs, Ann. Mat. Pura Appl. 91 (1972), 317–395. (1972) | MR 0312413 | Zbl 0231.53065

Ørsted B. Conformally invariant differential equations and projective geometry, J. Funct. Anal. 44 (1981), 1–23. (1981) | MR 0638292 | Zbl 0507.58048