Rankin–Cohen brackets and representations of conformal Lie groups

Michael Pevzner[1]

  • [1] University of Reims – FR 3399 CNRS Moulin de la Housse, BP 1037 F-51687, Reims France

Annales mathématiques Blaise Pascal (2012)

  • Volume: 19, Issue: 2, page 455-484
  • ISSN: 1259-1734

Abstract

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This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010.The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a non-commutative product induced on the set of holomorphic modular forms by a covariant quantization of the associate para-Hermitian symmetric space.

How to cite

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Pevzner, Michael. "Rankin–Cohen brackets and representations of conformal Lie groups." Annales mathématiques Blaise Pascal 19.2 (2012): 455-484. <http://eudml.org/doc/251123>.

@article{Pevzner2012,
abstract = {This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010.The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a non-commutative product induced on the set of holomorphic modular forms by a covariant quantization of the associate para-Hermitian symmetric space.},
affiliation = {University of Reims – FR 3399 CNRS Moulin de la Housse, BP 1037 F-51687, Reims France},
author = {Pevzner, Michael},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Rankin-Cohen brackets; Unitary representations; Conformal groups; Covariant quantization; unitary representations; conformal groups; covariant quantization},
language = {eng},
month = {7},
number = {2},
pages = {455-484},
publisher = {Annales mathématiques Blaise Pascal},
title = {Rankin–Cohen brackets and representations of conformal Lie groups},
url = {http://eudml.org/doc/251123},
volume = {19},
year = {2012},
}

TY - JOUR
AU - Pevzner, Michael
TI - Rankin–Cohen brackets and representations of conformal Lie groups
JO - Annales mathématiques Blaise Pascal
DA - 2012/7//
PB - Annales mathématiques Blaise Pascal
VL - 19
IS - 2
SP - 455
EP - 484
AB - This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010.The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a non-commutative product induced on the set of holomorphic modular forms by a covariant quantization of the associate para-Hermitian symmetric space.
LA - eng
KW - Rankin-Cohen brackets; Unitary representations; Conformal groups; Covariant quantization; unitary representations; conformal groups; covariant quantization
UR - http://eudml.org/doc/251123
ER -

References

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