Geodesic
Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 854-874

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of antiholomorphic sections in which the irreducible Hermitian representations of the original algebra are realized. The reproducing kernels of these spaces are expressed in terms of the Riemann theta function and its modifications. They generate quantum Kähler structures on the surface and the corresponding quantum reproducing measures. We construct coherent transforms intertwining abstract representations of an algebra with irreducible representations, and these transforms are also expressed via the theta function. 
@article{MZM_2001_70_6_a4,
     author = {M. V. Karasev and E. M. Novikova},
     title = {Coherent {Transforms} and {Irreducible} {Representations} {Corresponding} to {Complex} {Structures} on a {Cylinder} and on a {Torus}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {854--874},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a4/}
}
TY  - JOUR
AU  - M. V. Karasev
AU  - E. M. Novikova
TI  - Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus
JO  - Matematičeskie zametki
PY  - 2001
SP  - 854
EP  - 874
VL  - 70
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a4/
LA  - ru
ID  - MZM_2001_70_6_a4
ER  - 
%0 Journal Article
%A M. V. Karasev
%A E. M. Novikova
%T Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus
%J Matematičeskie zametki
%D 2001
%P 854-874
%V 70
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a4/
%G ru
%F MZM_2001_70_6_a4
M. V. Karasev; E. M. Novikova. Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 854-874. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a4/