论文标题
仿射Nil-Hecke代数和量子
Affine nil-Hecke algebras and Quantum cohomology
论文作者
论文摘要
令$ g $为一个紧凑的，连接的谎言组和$ t \ subset g $最大圆环。令$（m，ω）$为单调封闭的符号歧管，配备了$ g $的哈密顿动作。我们在$ s^1 \ s^1 \ times t $ equivariant量子共同体$ $，$ qH^*_ QH^*_ {s^1 _ {s^1 \ times times timiant Torrize for ham for ham for ham for Torruly to ham for ham ham for ham for ham nam nil-eftiratian nil-nil-hecke代数[OP，LJ]。我们表明，与阿贝尔情况一样，此动作在量子连接方面的行为很好。作为我们建筑的应用，我们表明，当$ g $是半简单时，$ g $ equivariant量子同时$ qh_g^*（m）$定义了一个规范性的holomorphic lagrangian subvarietian $ \ mathbb {l} _g（l} _g（m） bfm（g _ {\ mathbb {c}}}^{\ vee}）$在Langlands Dual Group的BFM空间中，证实了[T1]对Teleman的期望。
Let $G$ be a compact, connected Lie group and $T \subset G$ a maximal torus. Let $(M,ω)$ be a monotone closed symplectic manifold equipped with a Hamiltonian action of $G$. We construct a module action of the affine nil-Hecke algebra $\hat{H}_*^{S^1 \times T}(LG/T)$ on the $S^1 \times T$-equivariant quantum cohomology of $M$, $QH^*_{S^1 \times T}(M).$ Our construction generalizes the theory of shift operators for Hamiltonian torus actions [OP,LJ]. We show that, as in the abelian case, this action behaves well with respect to the quantum connection. As an application of our construction, we show that when $G$ is semi-simple, the $G$-equivariant quantum cohomology $QH_G^*(M)$ defines a canonical holomorphic Lagrangian subvariety $\mathbb{L}_G(M) \hookrightarrow BFM(G_{\mathbb{C}}^{\vee})$ in the BFM-space of the Langlands dual group, confirming an expectation of Teleman from [T1].
