Jacobson generators of (quantum) sl(n+1/m). Related statistics
by  T.D. Palev, N.I. Stoilova, J. Van der Jeugt

Abstract:
A description of the quantum superalgebra U_q[sl(n+1|m)] and in particular of the special linear superalgebra sl(n+1|m) via a new set of generators is given. It provides an alternative to the canonical description of U_q[sl(n+1|m)] in terms of Chevalley generators. The Jacobson generators satisfy threelinear supercommutation relations and define sl(n+1/m) (U_q[sl(n+1|m)]) as a (deformed) Lie supertriple system. The Pauli principle of the related statistics is formulated. It shows that the corresponding statistics belongs to the class of exclusion statistics in the sense that the number of available states on a certain orbital depends on the number of the already accommodated particles on the other orbitals.