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This article is cited in 4 scientific papers (total in 4 papers)
Representations of the twisted quantized enveloping algebra of type $C_n$
A. I. Molev University of Sydney
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.
Received: April 19, 2006
Citation:
A. I. Molev, “Representations of the twisted quantized enveloping algebra of type $C_n$”, Mosc. Math. J., 6:3 (2006), 531–551
Linking options:
https://www.mathnet.ru/eng/mmj259 https://www.mathnet.ru/eng/mmj/v6/i3/p531
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