Establishes generalized Howe dualities and fundamental theorems of invariant theory for Γ-graded gl(V(Γ,ω)), classifies unitarisable modules for two compact *-structures, constructs a Hopf (Γ,ω)-algebra, and realizes simple tensor modules via a Borel-Weil analogue.
Drinfeld realisations and vertex operator representations of quantum affine superalgebras
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abstract
Drinfeld realisations are constructed for the quantum affine superalgebras of the series ${\rm\mathfrak{osp}}(1|2n)^{(1)}$,${\rm\mathfrak{sl}}(1|2n)^{(2)}$ and ${\rm\mathfrak{osp}}(2|2n)^{(2)}$. By using the realisations, we develop vertex operator representations and classify the finite dimensional irreducible representations for these quantum affine superalgebras.
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Invariants and representations of the $\Gamma$-graded general linear Lie $\omega$-algebras
Establishes generalized Howe dualities and fundamental theorems of invariant theory for Γ-graded gl(V(Γ,ω)), classifies unitarisable modules for two compact *-structures, constructs a Hopf (Γ,ω)-algebra, and realizes simple tensor modules via a Borel-Weil analogue.