Communications in Mathematical Physics A Finite Analog of the AGT Relation I : Finite W-Algebras and Quasimaps ’ Spaces
Communications in Mathematical Physics A Finite Analog of the AGT Relation I : Finite W-Algebras and Quasimaps ’ Spaces
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数学物理中的通信 AGT 关系 I 的有限模拟：有限 W 代数和准映射空间
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
L. Rybnikov
中科院分区：
文献类型：
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作者：
A. Braverman;B. Feigin;M. Finkelberg;L. Rybnikov
最近，Alday，Gaiotto和Tchikawa[2]提出了一个猜想，将规范群G的四维超对称规范理论与某些二维共形场论联系起来。这个猜想暗示了P2上框架G-丛的模空间的Uhlenbeck部分紧化的(等变)交上同调上同调上存在某些结构。更确切地说，它预测了相应的W-代数在上述上同调上的作用的存在，满足某些性质。我们提出了AGT猜想(上述推论)的“有限类比”。也就是说，我们用从P1到G的任何部分标志簇G/P的基拟映射空间来代替Uhlenbeck空间，并猜想它的等变交上同调具有与P的Levi子群的李代数中的主幂零元素相关的有限W-代数U(g，e)的作用；这个作用有望满足某些自然性质列表。当P是Borel子群时，这个猜想推广了[5]的主要结果。我们用Brundan和Kleshchev的工作证明了我们关于G=GL(N)的猜想，他们用某些移位的延安解释了代数U(g，e)。
Recently Alday, Gaiotto and Tachikawa [2] proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain structures on the (equivariant) intersection cohomology of the Uhlenbeck partial compactification of the moduli space of framed G-bundles on P2. More precisely, it predicts the existence of an action of the corresponding W -algebra on the above cohomology, satisfying certain properties. We propose a “finite analog” of the (above corollary of the) AGT conjecture. Namely, we replace the Uhlenbeck space with the space of based quasi-maps from P1 to any partial flag variety G/P of G and conjecture that its equivariant intersection cohomology carries an action of the finite W -algebra U (g, e) associated with the principal nilpotent element in the Lie algebra of the Levi subgroup of P; this action is expected to satisfy some list of natural properties. This conjecture generalizes the main result of [5] when P is the Borel subgroup. We prove our conjecture for G = GL(N ), using the works of Brundan and Kleshchev interpreting the algebra U (g, e) in terms of certain shifted Yangians.