Biquantization of symmetric pairs and the quantum shift

Details Biquantization of symmetric pairs and the quantum shift Biquantization of symmetric pairs and the quantum shift

2011-05-30

arxiv.org/abs/1105.5973v1

Mathematics

Quantum Algebra

11 figures; comments are welcome

Scientific paper

The biquantization of symmetric pairs was studied in \cite{CT} in terms of Kontsevich-like graphs. This note, also in view of recent results in \cite{CFFR}, 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 \cite{CT} in view of the aforementioned correction by the quantum shift.

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