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Parabolic presentations of Yangian in types $B$ and $C$ (2502.21211v2)

Published 28 Feb 2025 in math.RT and math.QA

Abstract: We establish a parabolic presentation of the extended Yangian $\X(\mathfrak{g}{N})$ associated with the Lie algebras $\mathfrak{g}{N}$ of type $B$ and $C$, parameterized by a symmetric composition $\nu$ of $N$. By formulating a block matrix version of the RTT presentation of $\X(\mathfrak{g}{N})$, we systematically derive the generators and relations through the Gauss decomposition of the generator matrix in $\nu$-block form. Furthermore, leveraging this parabolic presentation, we obtain a novel formula for the center of $\X(\mathfrak{g}{N})$, offering new insights into its structure.

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