Biquantization techniques for computing characters of differential operators on Lie groups

Panagiotis Batakidis

doi:10.1016/j.crma.2010.11.012

Lie Algebras/Functional Analysis

Biquantization techniques for computing characters of differential operators on Lie groups

Presented by: Michel Duflo

Panagiotis Batakidis ¹

¹ Department of Mathematics, Aristotle University of Thessaloniki, Konstantinou Karamanli, Panepistimioupoli, 54124 Thessaloniki, Greece

Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 247-250.

Abstract
Résumé

We compare the character of the algebra $(U (g) / U {(g) h_{λ})}^{h}$ , as used by Fujiwara and Corwin and Greenleaf, with the character produced from biquantization techniques applied in the Lie case by Cattaneo and Torossian. We prove that up to a smaller (specialization) algebra, these two characters are the same. An old example is also treated and it is proved that we now get more information about the question of when the symmetrization is an isomorphism of algebras.

Nous comparons le caractère de lʼalgèbre $(U (g) / U {(g) h_{λ})}^{h}$ , tel quʼutilisé par Fujiwara et Corwin–Greenleaf, avec le caractère produit par les techniques de bi-quantification appliquées au cas des algèbres de Lie par Cattaneo–Torossian. Nous démontrons que ces deux caractères coïncident, à une algèbre (de spécialisation) plus petite près. Nous discutons également un exemple bien connu et nous obtenons des informations supplémentaires quant à la question de savoir si la symétrisation est un isomorphisme dʼalgèbres.

Received: 2010-09-23
Accepted: 2010-11-10
Published online: 2010-12-30

DOI: 10.1016/j.crma.2010.11.012

Author's affiliations:

Panagiotis Batakidis ¹

¹ Department of Mathematics, Aristotle University of Thessaloniki, Konstantinou Karamanli, Panepistimioupoli, 54124 Thessaloniki, Greece

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     title = {Biquantization techniques for computing characters of differential operators on {Lie} groups},
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Panagiotis Batakidis. Biquantization techniques for computing characters of differential operators on Lie groups. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 247-250. doi : 10.1016/j.crma.2010.11.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.012/

References
Cited by

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