旗簇上纵向伪微分算子的乘积
Products of longitudinal pseudodifferential operators on flag varieties
摘要：
与$SL(n,\mathbb{C})$的单根的每个集合$S$相关联的是$\mathbb{C}^n$的完全标志的空间$X$的等变纤维化$X\to X_S$。对于每个这样的纤维化，我们关联一个代数$J_S$的运营商$L^2(X)$，其中包含，特别是纵向pseudodiomatic运营商的负阶正切的纤维。它们形成了一个算子理想的格，其公共交集是紧算子。因此，（例如）沿着两个这样的纤维化，$X\to X_S$和$X\to X_T$的纤维的纤维平滑算子的乘积是紧算子，如果$S\cup T$是单根的全集。该结构使用非交换调和分析，并取决于SU（n）子群的表示论性质，这可以被描述为“子表示的基本正交性”。
英文摘要：
Associated to each set $S$ of simple roots for $SL(n,\mathbb{C})$ is an equivariant fibration $X\to X_S$ of the space $X$ of complete flags of $\mathbb{C}^n$. To each such fibration we associate an algebra $J_S$ of operators on $L^2(X)$ which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the compact operators. As a consequence, the product of fibrewise smoothing operators (for instance) along the fibres of two such fibrations, $X\to X_S$ and $X\to X_T$, is a compact operator if $S\cup T$ is the full set of simple roots. The construction uses noncommutative harmonic analysis, and hinges upon a representation theoretic property of subgroups of SU(n), which may be described as `essential orthogonality of subrepresentations'.
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。
