## 孙娟娟: Polynomial relations of \$q\$-characters

：孙娟娟 博士

In the finite dimensional representation theory of quantum affine algebras, the well-known Kirillov-Reshetikhin modules satisfy the so-called \$T\$-system. A natural consideration is to give a \$q\$-analogue of the \$T\$-system. More explicitly, let \$U_q(X^{(1)}_n)\$ be a quantum affine algebra, and let \$U_q(\mathfrak{b})\$ be its Borel subalgebra, via the ODE/IM correspondence,  we give conjectural polynomial relations among the \$q\$-characters of certain representations of the Borel subalgebras.