Geodesic
A Description of Smooth Vectors of the Weil Representation in the Geometric Realization
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 90-93 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe the image of the Weil representation of the double covering of the symplectic group in the Schwartz space in the so-called geometric realization, i.e., in holomorphic functions on the symmetric domain called the Siegel upper half-plane.
Keywords: Weil representation, Schwartz space, Siegel upper half-plane. 
@article{FAA_2006_40_3_a12,
     author = {A. V. Stoyanovskii},
     title = {A {Description} of {Smooth} {Vectors} of the {Weil} {Representation} in the {Geometric} {Realization}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {90--93},
     year = {2006},
     volume = {40},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a12/}
}
TY  - JOUR
AU  - A. V. Stoyanovskii
TI  - A Description of Smooth Vectors of the Weil Representation in the Geometric Realization
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2006
SP  - 90
EP  - 93
VL  - 40
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a12/
LA  - ru
ID  - FAA_2006_40_3_a12
ER  - 
%0 Journal Article
%A A. V. Stoyanovskii
%T A Description of Smooth Vectors of the Weil Representation in the Geometric Realization
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2006
%P 90-93
%V 40
%N 3
%U http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a12/
%G ru
%F FAA_2006_40_3_a12
A. V. Stoyanovskii. A Description of Smooth Vectors of the Weil Representation in the Geometric Realization. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 90-93. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a12/

[1] Zh. Lion, M. Vern, Predstavlenie Veilya, indeks Maslova i teta-ryady, Mir, M., 1983 | MR | Zbl

[2] Yu. A. Neretin, Contemporary Mathematical Physics, Transl. Amer. Math. Soc. Ser. 2, 175, 1996, 97–135 | MR | Zbl

[3] L. Khërmander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, t. 3, Mir, M., 1987 | MR

[4] Yu. A. Neretin, http://arxiv.org/math.RT/0012220

[5] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii. Vyp. 2. Prostranstva osnovnykh i obobschennykh funktsii, Fizmatgiz, M., 1958 | MR | Zbl