论文标题
量子仿射代数的有限维表示的三角k-矩阵
Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为一个复杂的简单谎言代数，$ u_q \ hat {\ mathfrak {g}} $相应的量子仿射代数。我们证明，每个不可约有的有限维$ u_q \ hat {\ mathfrak {g}} $ - 模块都会产生一个三角k-矩阵的家族，即Cherednik的广义重新填充方程的理性解决方案。结果取决于选择量子仿射对对称对$ u_q \ mathfrak {k} \ subset u_q \ hat {\ mathfrak {g}} $。它取决于为任意量子对称对的通用k- matrices的构建，并依赖于证明每个不可约$ u_q \ hat {\ mathfrak {\ mathfrak {g}} $ - 在$ u_q {\ mathfrak {K k}} $下，通常不可限制地限制在限制下。对于小模块和Kirillov-Reshetikhin模块，我们获得了标准和转置反射方程的新解决方案。
Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_q\hat{\mathfrak{g}}$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q\hat{\mathfrak{g}}$-module gives rise to a family of trigonometric K-matrices, i.e., rational solutions of Cherednik's generalized reflection equation. The result depends upon the choice of a quantum affine symmetric pair $U_q\mathfrak{k}\subset U_q\hat{\mathfrak{g}}$. It hinges on the construction of universal K-matrices for arbitrary quantum symmetric pairs, and relies on proving that every irreducible $U_q\hat{\mathfrak{g}}$-module is generically irreducible under restriction to $U_q{\mathfrak{k}}$. In the case of small modules and Kirillov-Reshetikhin modules, we obtain new solutions of the standard and the transposed reflection equations.
