Factor representations of the infinite spin-symmetric group

Let S() be the group of finite permutations of the sequence of natural numbers. The infinite spin-symmetric group T() is its central Z₂-extension. With the aid of this extension the projective representations of the group S() can be linearized. The paper describes the factor representation of type II₁ of the group T().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 181, pp. 132–145, 1990.