扭Dirac算子的表示论嵌入
Representation theoretic embedding of twisted Dirac operators
摘要：
设$G$是具有有限中心的非紧连通半单实李群.设$L$是$G$的一个非紧连通闭子群，它传递地作用在对称空间$G/H$上，使得$L\cap H$是紧的.本文研究了Dirac算符$D_{G/H}(E)$作用于$G/H$上自旋丛的$E$ -扭曲截面对$L/L\cap H$的作用.作为副产品，在$(G,H,L)=(SL(2,{\mathbb R})\times SL(2,{\mathbb R}),Δ(SL(2,{\mathbb R})\times SL(2,{\mathbb R})),SL(2,{\mathbb R})\times SO(2))$的情况下，我们确定了位于$D_{G/H}(E)$的内核中的$L$的某些表示。
英文摘要：
Let $G$ be a non-compact connected semisimple real Lie group with finite center. Suppose $L$ is a non-compact connected closed subgroup of $G$ acting transitively on a symmetric space $G/H$ such that $L\cap H$ is compact. We study the action on $L/L\cap H$ of a Dirac operator $D_{G/H}(E)$ acting on sections of an $E$-twist of the spin bundle over $G/H$. As a byproduct, in the case of $(G,H,L)=(SL(2,{\mathbb R})\times SL(2,{\mathbb R}),Δ(SL(2,{\mathbb R})\times SL(2,{\mathbb R})),SL(2,{\mathbb R})\times SO(2))$, we identify certain representations of $L$ which lie in the kernel of $D_{G/H}(E)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
