论文标题
PBW理论方法量子代数的模块类别
PBW theoretic approach to the module category of quantum affine algebras
论文作者
论文摘要
令$ u_q'（\ mathfrak {g}）$为未介绍的仿射类型的量子仿射代数，让$ \ mathcal {c}^0 _ {\ mathfrak {g}} $ be hernandez-leclerc的类别。对于双重性，$ \ MATHCAL {D} $中的$ \ Mathcal {C}^0 _ {\ Mathfrak {g}} $，我们用$ \ Mathcal {f} _ {\ Mathcal {\ Mathcal {d}} $量化量子offinum opjectine weyl-schur-schur-schur-schur-schur-schur-schur duality functor。我们为二元数据$ \ MATHCAL {D} $提供足够的条件，以提供函数$ \ MATHCAL {F} _ {\ MATHCAL {D}} $将简单模块发送到简单模块。然后，我们在$ \ Mathcal {C}^0 _ {\ Mathfrak {g}} $中介绍了cuspidal模块的概念，并证明所有简单的模块$ \ Mathcal {c}^0 _ {\ Mathfrak {g}} $都可以按订单的consors os os osed osed consore consore consore consore consore consore consore consore consore consore consore cosed cosed cosed cosed cosed cosed consors osed。
Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of untwisted affine ADE type and let $\mathcal{C}^0_{\mathfrak{g}}$ be Hernandez-Leclerc's category. For a duality datum $\mathcal{D}$ in $\mathcal{C}^0_{\mathfrak{g}}$, we denote by $\mathcal{F}_{\mathcal{D}}$ the quantum affine Weyl-Schur duality functor. We give sufficient conditions for a duality datum $\mathcal{D}$ to provide the functor $\mathcal{F}_{\mathcal{D}}$ sending simple modules to simple modules. Then we introduce the notion of cuspidal modules in $\mathcal{C}^0_{\mathfrak{g}}$, and show that all simple modules in $\mathcal{C}^0_{\mathfrak{g}}$ can be constructed as the heads of ordered tensor products of cuspidal modules.
