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تسجيل مستخدم جديدPBW theoretic approach to the module category of quantum affine algebras
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Let $U_q(mathfrak{g})$ be a quantum affine algebra of untwisted affine ADE type and let $mathcal{C}^0_{mathfrak{g}}$ be Hernandez-Leclercs 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.
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Let $mathfrak{g}_0$ be a simple Lie algebra of type ADE and let $U_q(mathfrak{g})$ be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group $B(mathfrak{g}_0)$ on the quantum Grothendieck ring $K_t(
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