On the Generalized Exclusion Statistics

Abstract

We review the principal steps leading to drive the wave function ${\psi }_{\{k_1,k_2,...,k_N\}}(1,2,...,N)$ of a gaz of $N$ identical particle states with exotic statistics. For spins $s=1/M$ $mod(1)$, we show that the quasideterminant conjectured in [19], by using $2d$ conformal field theoretical methods, is indeed related to the quantum determinant of noncommutative geometry. The q-number $[N]!={\prod }_{n=1}^N({\sum }_{j=0}^{N-1}{q}^j)$ carrying the effect of the generalized Pauli exclusion principle, according to which no more than $(M-1)$ identical particles of spin $s=1/M$ $mod(1)$ can live altogether on the same quantum state, is rederived in rigourous from the q-antisymmetry. Other features are also given.

13 pages, Latex. To be submitted to Journal of Math. Phys