Quantization of Hamiltonian loop group spaces
Quantization of Hamiltonian loop group spaces
复制标题
哈密顿环群空间的量化
作者：
Yiannis Loizides;Yanli Song
证明了非紧流形上的自旋-c Dirac算子$$\mathsf {D}$$ D在半直积群$$K\ltimes \Gamma $$ K <e:1> Γ （K紧且$$\Gamma $$ Γ离散）的作用下满足一定条件的Fredholm性质。我们将这一结果应用于哈密顿循环群空间理论中的一个例子。在这种情况下，我们证明了某个索引对$$[{\mathcal {X}}] \cap [\mathsf {D}]$$ [X]∩[D]产生极大环面的表示环的形式补全$$R^{-\infty }(T)$$ R-∞(T)的一个元素$$T \subset H$$ T∧H；得到的元素在仿射Weyl群的作用下具有额外的反对称性质，表明$$[{\mathcal {X}}] \cap [\mathsf {D}]$$ [X]∩[D]对应于环群的射影正能量表示环中的一个元素。
We prove a Fredholm property for spin-c Dirac operators $$\mathsf {D}$$D on non-compact manifolds satisfying a certain condition with respect to the action of a semi-direct product group $$K\ltimes \Gamma $$K⋉Γ, with K compact and $$\Gamma $$Γ discrete. We apply this result to an example coming from the theory of Hamiltonian loop group spaces. In this context we prove that a certain index pairing $$[{\mathcal {X}}] \cap [\mathsf {D}]$$[X]∩[D] yields an element of the formal completion $$R^{-\infty }(T)$$R-∞(T) of the representation ring of a maximal torus $$T \subset H$$T⊂H; the resulting element has an additional antisymmetry property under the action of the affine Weyl group, indicating $$[{\mathcal {X}}] \cap [\mathsf {D}]$$[X]∩[D] corresponds to an element of the ring of projective positive energy representations of the loop group.
哈密顿环群空间的旋量模
影响因子：
0.7
作者：
Loizides, Yiannis;Meinrenken, Eckhard;Song, Yanli
通讯作者：
Song, Yanli