论文标题
派生的代表方案和中岛Quiver品种
Derived Representation Schemes and Nakajima Quiver Varieties
论文作者
论文摘要
我们介绍了与箭袋相关的派生表示方案，该方案可能被认为是Nakajima品种的派生版本。我们展示了派生的表示方案作为Koszul复合物的明确模型，因此我们表明，当且仅当定义相应的Nakajima品种的时刻映射时，它就消失了更高的同源性。在这种情况下，我们证明了代表方案的同种型组件的比较定理，用于纳卡吉玛品种上的重言式捆绑包的k理论类别。作为这种结果的必然性，我们从几年开始就获得了数学和物理文献中存在的一些积分公式，例如$ s^4 $上构成Instantons的Moduli Space的Nekrasov分区函数的公式。在技术方面，我们通过引入与一般线性群的还原亚组相关的衍生部分特征方案，扩展了相对衍生的表示方案的理论，并构建了代数的派生表示代表函数的均等版本，并具有代数圆锥形的合理作用。
We introduce a derived representation scheme associated with a quiver, which may be thought of as a derived version of a Nakajima variety. We exhibit an explicit model for the derived representation scheme as a Koszul complex and by doing so we show that it has vanishing higher homology if and only if the moment map defining the corresponding Nakajima variety is flat. In this case we prove a comparison theorem relating isotypical components of the representation scheme to equivariant K-theoretic classes of tautological bundles on the Nakajima variety. As a corollary of this result we obtain some integral formulas present in the mathematical and physical literature since a few years, such as the formula for Nekrasov partition function for the moduli space of framed instantons on $S^4$. On the technical side we extend the theory of relative derived representation schemes by introducing derived partial character schemes associated with reductive subgroups of the general linear group and constructing an equivariant version of the derived representation functor for algebras with a rational action of an algebraic torus.
