Simple Weight Modules For Twisted Yangian Y（sp₂）

Let g be a finite-dimensional complex simple Lie algebra.Yangian Y（g）and Quantum affine algebras U_q（?）form two very important infinite-dimensional affine quantum groups.Their repre-sentation theory is a very popular research direction.Yangian module focuses on Verma modules and finite-dimensional irreducible modules.In recent years,in the study of bounded integrable sys-tems,The module of Twisted Yangian Y（g_N）is a weight module if it is weight module of its sub-algebra U（g_N）.We constructed a class of infinite-dimensional simple weight modules of Y（sp₂）,classifying Y（sp₂）simple weight modules with a one-dimensional space.Yangian Y（gl_N）’s coideal subalgebra Y（g_N）,is getting more and more attention and research.The module of Twisted Yan-gian Y（g_N）is a weight module if it is weight module of its subalgebra U（g_N）.We constructed a class of infinite-dimensional simple weight modules of Y（sp₂）,classifying Y（sp₂）simple weight modules with a one-dimensional space.