Geodesic
Holomorphic extensions of representations of the~group of the~diffeomorphisms of the~circle
Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 75-97

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

This paper gives the construction of a semigroup $\Gamma$ which could be thought of as the complexincation of the group $\operatorname{Diff}$ of analytic diffeomorphisms of the circle, and it is shown that any unitary projective representation of $\operatorname{Diff}$ with highest weight has a holomorphic extension to $\Gamma$. For this, $\Gamma$ is embedded in the semigroup of “endomorphisms of canonical commutation relations” (this is a certain part of the Lagrange Grassmannian in complex symplectic Hilbert space). Bibliography: 25 titles. 
@article{SM_1990_67_1_a4,
     author = {Yu. A. Neretin},
     title = {Holomorphic extensions of representations of the~group of the~diffeomorphisms of the~circle},
     journal = {Sbornik. Mathematics},
     pages = {75--97},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_1_a4/}
}
TY  - JOUR
AU  - Yu. A. Neretin
TI  - Holomorphic extensions of representations of the~group of the~diffeomorphisms of the~circle
JO  - Sbornik. Mathematics
PY  - 1990
SP  - 75
EP  - 97
VL  - 67
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1990_67_1_a4/
LA  - en
ID  - SM_1990_67_1_a4
ER  - 
%0 Journal Article
%A Yu. A. Neretin
%T Holomorphic extensions of representations of the~group of the~diffeomorphisms of the~circle
%J Sbornik. Mathematics
%D 1990
%P 75-97
%V 67
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1990_67_1_a4/
%G en
%F SM_1990_67_1_a4
Yu. A. Neretin. Holomorphic extensions of representations of the~group of the~diffeomorphisms of the~circle. Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 75-97. http://geodesic.mathdoc.fr/item/SM_1990_67_1_a4/