论文标题
Q-Character的Weyl群对称性
Weyl group symmetry of q-characters
论文作者
论文摘要
我们定义了一个简单的谎言代数g的weyl oft w的作用，这是环y的完成，这是相应的量子仿射代数u_q（g^）的q字符同态同态的代码。我们证明，Y的Winvariants的子恰好是Q-Character的环，这与U_Q（g^）有限维表示的类别类别的Grothendieck环是同构。这解决了Q-Characters理论中的一个旧难题。我们还确定了以前用来描述Q字符环的筛选操作员，它们是在一定限制下从W中进行简单反射的二次术语。我们的结果已经在ARXIV中的U_Q（G^）的弓形体subsalgebra类别的研究中找到了应用：2312.13256以及Arxiv中群集代数的分类：2401.04616。
We define an action of the Weyl group W of a simple Lie algebra g on a completion of the ring Y, which is the codomain of the q-character homomorphism of the corresponding quantum affine algebra U_q(g^). We prove that the subring of W-invariants of Y is precisely the ring of q-characters, which is isomorphic to the Grothendieck ring of the category of finite-dimensional representations of U_q(g^). This resolves an old puzzle in the theory of q-characters. We also identify the screening operators, which were previously used to describe the ring of q-characters, as the subleading terms of simple reflections from W in a certain limit. Our results have already found applications to the study of the category O of representations of the Borel subalgebra of U_q(g^) in arXiv:2312.13256 and to the categorification of cluster algebras in arXiv:2401.04616.
