Spectrum generating on twistor bundle

Thomas Branson; Doojin Hong

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 169-183
  • ISSN: 0044-8753

Abstract

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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 × 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.

How to cite

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Branson, Thomas, and Hong, Doojin. "Spectrum generating on twistor bundle." Archivum Mathematicum 042.5 (2006): 169-183. <http://eudml.org/doc/249798>.

@article{Branson2006,
abstract = {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.},
author = {Branson, Thomas, Hong, Doojin},
journal = {Archivum Mathematicum},
keywords = {conformal geometry; spinors; twistor; intertwinors; Dirac operator; spectrum of Dirac operator},
language = {eng},
number = {5},
pages = {169-183},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Spectrum generating on twistor bundle},
url = {http://eudml.org/doc/249798},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Branson, Thomas
AU - Hong, Doojin
TI - Spectrum generating on twistor bundle
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 169
EP - 183
AB - 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.
LA - eng
KW - conformal geometry; spinors; twistor; intertwinors; Dirac operator; spectrum of Dirac operator
UR - http://eudml.org/doc/249798
ER -

References

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  5. 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) MR1367629
  6. Hong D., Eigenvalues of Dirac and Rarita-Schwinger operators, Clifford Algebras and their Applications in Mathematical Physics, Birkhäuser, 2000. Zbl1080.53044MR2025981
  7. Hong D., Spectra of higher spin operators, Ph.D. Dissertation, University of Iowa, 2004. MR2706219
  8. Kosmann Y., Dérivées de Lie des spineurs, Ann. Mat. Pura Appl. 91 (1972), 317–395. (1972) Zbl0231.53065MR0312413
  9. Ørsted B., Conformally invariant differential equations and projective geometry, J. Funct. Anal. 44 (1981), 1–23. (1981) Zbl0507.58048MR0638292

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