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Biquantization of symmetric pairs and the quantum shift


Cattaneo, Alberto S; Rossi, Carlo Antonio; Torossian, Charles (2013). Biquantization of symmetric pairs and the quantum shift. Journal of Geometry and Physic, 74:211-250.

Abstract

The biquantization of symmetric pairs was studied by Cattaneo etal. (2008) [1] in terms of Kontsevich-like graphs. This note, also in view of recent results by Calaque etal. (2009) [3], amends a minor mistake that did not spoil the main results of the paper. The mistake consisted in ignoring a regular term in the boundary contribution of some propagators. On the other hand, its correction brings back the quantum shift, present in the approaches by the orbit method, that was otherwise puzzlingly missing. In addition a detailed comparison of the two, equivalent, ways of defining biquantization working on the upper half plane or on one quadrant is presented, as well as a more conceptual approach to biquantization and the due corrections of some results of Cattaneo etal. (2008) [1] in view of the aforementioned correction by the quantum shift.

Abstract

The biquantization of symmetric pairs was studied by Cattaneo etal. (2008) [1] in terms of Kontsevich-like graphs. This note, also in view of recent results by Calaque etal. (2009) [3], amends a minor mistake that did not spoil the main results of the paper. The mistake consisted in ignoring a regular term in the boundary contribution of some propagators. On the other hand, its correction brings back the quantum shift, present in the approaches by the orbit method, that was otherwise puzzlingly missing. In addition a detailed comparison of the two, equivalent, ways of defining biquantization working on the upper half plane or on one quadrant is presented, as well as a more conceptual approach to biquantization and the due corrections of some results of Cattaneo etal. (2008) [1] in view of the aforementioned correction by the quantum shift.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:December 2013
Deposited On:22 Nov 2013 11:37
Last Modified:05 Apr 2016 17:10
Publisher:Elsevier
ISSN:0393-0440
Publisher DOI:https://doi.org/10.1016/j.geomphys.2013.07.001

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