Typical representations of Takiff superalgebras

We investigate representations of the Takiff superalgebras , for , associated with a basic classical and a periplectic Lie superalgebras . We introduce the odd reflections and formulate a general notion of typical representations of the Takiff superalgebras . As a consequence, we provide a complete description of the characters of the finite‐dimensional modules over type I Takiff superalgebras. For the Lie superalgebras and , we prove that the Kac induction functor of leads to an equivalence from an arbitrary typical Jordan block of the category for to a Jordan block of the category for the even subalgebra of . We also obtain a classification of non‐singular simple Whittaker modules over the Takiff superalgebras.