We realize the Weil representation of infinite dimensional symplectic group
and spinor representation of infinite-dimensional group $GL$ by linear
operators in the space of symmetric functions in infinite number of variables.
@article{0306077,
author = {Neretin, Yurii A.},
title = {Structures of boson and fermion Fock spaces in the space of symmetric
functions},
journal = {arXiv},
volume = {2003},
number = {0},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/0306077}
}
Neretin, Yurii A. Structures of boson and fermion Fock spaces in the space of symmetric
functions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306077/