标题： 分阶段约简的仿射W代数 显示英文标题

标题： Reduction by stages for affine W-algebras

摘要： 给定一个单李代数中的幂零轨道对，可以关联一对称为仿射W-代数的顶点代数。 在这些轨道的一些兼容条件之下，我们证明其中一个W-代数可以作为另一个W-代数的量子哈密顿约化得到。 这个性质被称为分阶段约化。 我们在经典类型和例外类型中提供了几个例子。 为了证明仿射W-代数的分阶段约化，我们利用了之前关于与这些幂零轨道相关的Slodowy截面的分阶段约化的研究成果，这些截面是W-代数的关联品种。 我们还证明并使用了这样一个事实：每个W-代数可以使用几种等价的BRST上同调构造来定义：选择合适的BRST复形可以使这两个W-代数以自然的方式连接起来。 显示英文摘要

摘要： Given a pair of nilpotent orbits in a simple Lie algebra, one can associate a pair of vertex algebras called affine W-algebras. Under some compatibility conditions on these orbits, we prove that one of these W-algebras can be obtained as the quantum Hamiltonian reduction of the other. This property is called reduction by stages. We provide several examples in classical and exceptional types. To prove reduction by stages for affine W-algebras, we use our previous work on reduction by stages for the Slodowy slices associated with these nilpotent orbits, these slices being the associated varieties of the W-algebras. We also prove and use the fact that each W-algebra can be defined using several equivalent BRST cohomology constructions: choosing the right BRST complexes allows us to connect the two W-algebras in a natural way.