论文标题
最小nilpotent轨道中仿射顶点代数的简单模块
Simple modules for Affine vertex algebras in the minimal nilpotent orbit
论文作者
论文摘要
我们以Gelfand-tsetlin Tableaux的方式明确构建了一个简单的正能代表的新家族，用于简单的仿射顶点代数V_K（Sl_ {n+1}）在SL_ {n+1}的最小nilpotent Orbit中。这些表示是Sl_n+1的仿射Kac-Moody代数上的诱导模块的商，尤其包括所有可接受的简单最高权重模块和SL_2引起的所有简单模块。最小的nilpotent轨道中的任何此类简单模块都具有界限的重量。
We explicitly construct, in terms of Gelfand--Tsetlin tableaux, a new family of simple positive energy representations for the simple affine vertex algebra V_k(sl_{n+1}) in the minimal nilpotent orbit of sl_{n+1}. These representations are quotients of induced modules over the affine Kac-Moody algebra of sl_n+1 and include in particular all admissible simple highest weight modules and all simple modules induced from sl_2. Any such simple module in the minimal nilpotent orbit has bounded weight multiplicities.
