  Generalized quantum statistics will be presented in the context of
representation theory of Lie (super)algebras. This approach provides a natural
mathematical framework, as is illustrated by the relation between para-Bose and
para-Fermi operators and Lie (super)algebras of type B. Inspired by this
relation, A-statistics is introduced, arising from representation theory of the
Lie algebra A_n. The Fock representations for A_n=sl(n+1) provide microscopic
descriptions of particular kinds of exclusion statistics, which may be called
quasi-Bose statistics. It is indicated that A-statistics appears to be the
natural statistics for certain lattice models in condensed matter physics.
