Parabolic presentations of Yangian in types B and C

2025/02/28 by Chang, Zhihua, Jing, Naihuan, Liu, Ming +1
#FOS: Mathematics #Primary: 17B37 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #secondary: 81R51

paper · doi:10.48550/arxiv.2502.21211

Abstract

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

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