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A note on the quantum Berezinian for the double Yangian of the Lie superalgebra $\mathfrak{gl}_{m|n}$
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abstract
In this note, we generalize the notion of quantum Berezinian to the double Yangian ${\rm DY}(\mathfrak{gl}_{m|n})$ of the Lie superalgebra $\mathfrak{gl}_{m|n}$. We show that its coefficients form a family of algebraically independent topological generators of the center of ${\rm DY}(\mathfrak{gl}_{m|n})$.
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Cited by 2 Pith papers
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Quantum Sugawara operators in $\mathrm{U}_q(\widehat{\mathfrak{gl}}_{M|N})$
Sugawara operators for the quantum affine superalgebra U_q(gl_{M|N}) are shown to be central at the critical level, with Harish-Chandra images expressed as sums over semistandard tableaux.
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Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{M|N}$, II: Quantum currents
The authors extend the Etingof-Kazhdan quantum vertex algebra construction and the critical-level central element construction from the double Yangian of gl_M to the Lie superalgebra gl_{M|N}.
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