Characters of typical irreducible finite-dimensional q(n) -modules

Degenerate affine Hecke–Clifford algebras and type Q Lie superalgebras

“…The main difficulty is a lack of information about the category O(q(n)). The category of finite dimensional representations of q(n) has been studied by Penkov and Serganova [28][29][30]; they give a character formula for all finite dimension simple q(n)-modules. Using other methods, Brundan [3] has also studied this category, and has even obtained some (conjectural) information about the whole category O(q(n)) via the theory of crystals.…”

“…Moreover, it is known L(λ) is finite dimensional if, and only if, λ ∈ P + rat (see [28]). The following lemma seems standard, but we cannot find it stated in the literature.…”

“…First we recall the following key result of Penkov [28]. Given a weight λ ∈ P, we write χ λ for the central character defined by the simple q(n)-module of highest weight λ.…”

“…The question then becomes to describe when χ λ = χ μ for λ, μ ∈ P. This is answered in the case when λ is typical by the following result of Penkov [28]. Recall that the symmetric group acts on P by permuation of coordinates.…”

Fock representations of the Lie superalgebraq(n+1)

“…Also this Lie superalgebra has received attention recently. In particular, characters of finite-dimensional irreducible graded representations of q(n) have been determined [17,18,19], both in the typical and atypical case. In a different context, oscillator realizations have been given [20].…”