Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 2, 193-204.
Remarks to the Dimension of an Atypical Irreducible Representation of the
Special Lie Superalgebra sl(1,n)
Hartmut Schlosser
In [6] and [7] Palev gave explicit expressions for the action of the
generators of the Lie superalgebra $sl(1,n)$ at an (irreducible)
representation. His description of the representation space W of an atypical
irreducible representation in terms of highest weights of $gl(n)$
representations give a possibility to compute the dimension of W numerically.
In this paper we will proof an explicit formula for the dimension of an
atypical representation of
$sl(1,n)$ using numbers $H_l$ which connect with the
Bernoulli numbers $B_l$.