论文标题
元容器和自旋表示：平行处理
Metaplectic and spin representations: a parallel treatment
论文作者
论文摘要
符号和正交组之间的类比，被认为是实际双线性形式的对称性，在其（元容器和自旋）射击表示中都表现出来。在有限的维度中，这些是双重覆盖组的真实表示。但是一个人也可以通过一个圆圈使用组扩展。在这里，我们布置了MP $^\ Mathrm {C} $和Spin $^\ Mathrm {C} $覆盖组的平行处理，并通过在相应的Fock空间上作用，通过置换某些高斯矢量。这些扩展的共生表现出有趣的相似性。
The analogies between symplectic and orthogonal groups, regarded as symmetries of real bilinear forms, are manifest in their (metaplectic and spin) projective representations. In finite dimensions, those are true representations of doubly covering groups; but one may also use group extensions by a circle. Here we lay out a parallel treatment of of the Mp$^\mathrm{c}$ and Spin$^\mathrm{c}$ covering groups, acting on the respective Fock spaces by permuting certain Gaussian vectors. The cocycles of these extensions exhibit interesting similarities.
