ON CERTAIN STATES ON FREE ASTERISK-ALGEBRAS AND THEIR GNS REPRESENTATIONS

States on free -algebras expressed in terms of ordered partitions are studied. To this class belong twisted limit states that are derived f rom a convolution type q-analog of the quantum central Limit theorem ( qclt) for twisted free -bialgebras C-q, studied previously in the cas e of quantum groups. A special form of the GNS representation in terms of generalized creation and annihilation operators, A(v) and A(v), r espectively, living in the infinite tenser product of Hilbert spaces i s given leading to a generalization of the Fock space. It is also show n that another family of states of similar combinatorics can be obtain ed from the convolution series. (C) 1995 American Institute of Physics .