论文标题
量子共轭类别的向量捆绑包
Vector bundles on quantum conjugacy classes
论文作者
论文摘要
令$ \ mathfrak {g} $为一个经典类型的简单复杂的谎言代数，$ u_q（\ mathfrak {g}）$在$ q $ in $ q $的相应的drinfeld-jimbo Quantum group不是一个团结的根。固定的最大圆环$ t $ t $的每个点$ t $ t $与lie代数$ \ mathfrak {g} $的lie代数$ g $一起，我们将添加剂类别$ \ mathcal {o} {o} _q（t）$ $ u_q（\ mathfrak {g}）$ - 模块化与finitial ins copredity fin fin fin fin $ U_Q（\ Mathfrak {G}）$ - 模块。我们证明$ \ Mathcal {o} _q（t）$本质上是半简单的，并使用它来明确量化$ t $的共轭类别上的ecurivariant vector捆绑包。
Let $\mathfrak{g}$ be a simple complex Lie algebra of a classical type and $U_q(\mathfrak{g})$ the corresponding Drinfeld-Jimbo quantum group at $q$ not a root of unity. With every point $t$ of the fixed maximal torus $T$ of an algebraic group $G$ with Lie algebra $\mathfrak{g}$ we associate an additive category $\mathcal{O}_q(t)$ of $U_q(\mathfrak{g})$-modules that is stable under tensor product with finite-dimensional quasi-classical $U_q(\mathfrak{g})$-modules. We prove that $\mathcal{O}_q(t)$ is essentially semi-simple and use it to explicitly quantize equivariant vector bundles on the conjugacy class of $t$.
