  The properties of A-statistics, related to the class of simple Lie algebras
sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are
further investigated. The description of each sl(n+1) is carried out via
generators and their relations, first introduced by Jacobson. The related Fock
spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The
Pauli principle of the underlying statistics is formulated. In addition the
paper contains the following new results: (a) The A-statistics are interpreted
as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ...,
B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is
proved that in an appropriate topology the limit of B(p)_i^\pm for p going to
infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation
operators; (c) It is shown that the local statistics of the degenerated
hard-core Bose models and of the related Heisenberg spin models is p=1
A-statistics.
