Abstract:
We prove a version of the Poincaré–Birkhoff–Witt theorem for the twisted quantized enveloping algebra ${\rm U}'_q(\mathfrak{sp}_{2n})$. This is a subalgebra of ${\rm U}_q(\mathfrak{sp}_{2n})$ and a deformation of the universal enveloping algebra ${\rm U}(\mathfrak{sp}_{2n})$ of the symplectic Lie algebra. We classify finite-dimensional irreducible representations of ${\rm U}'_q(\mathfrak{sp}_{2n})$ in terms of their highest weights and show that these representations are deformations of finite-dimensional irreducible representations of $\mathfrak{sp}_{2n}$.
Key words and phrases:Quantized enveloping algebra, symplectic Lie algebra, representation.
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