DEFORMED FOCK SPACES, HECKE OPERATORS AND MONOTONE FOCK SPACE OF MURAKI

The main purpose of this paper is to extend our previous construction of T-Fock spaces from a given Yang-Baxter operator satisfying the inequalities-1 <= T <= 1 to the constructions of T-symmetric Fock spaces related to the class of Yang-BaxterHecke operators meeting a weaker condition that T >=-1. The new representation of the monotone Fock space of N. Muraki will be given. The main idea of this paper is the new class of generalized Gaussian random variables acting on suitable T-symmetric Fock spaces. Relations with the row and column operator space will be also given.