青年学术论坛邀请报告

摘要：We extend an inhomogeneous polynomial representation of special linear
Lie superalgebras sl(m + 1|n) to an inhomogeneous representation on the
tensor space of any irreducible tensor representation of the general linear
Lie superalgebras gl(m|n) with this polynomial space via Shen’s mixed
product. We find a sufficient and necessary condition for irreducibility of
these inhomogeneous representations, and get the Jordan-H¨older series of
those which are not irreducible. Furthermore, we point out that all these
irreducible modules are lowest weight modules. Their lowest weights and
character formulas are obtained.