A mirror symmetric solution to the quantum Toda lattice

仿射Toda系统 的镜像对称性

Mirror Symmetry of the Affine Toda Systems

本文研究了复可约群G的仿射Toda系统的镜像对称性，通过证明缠绕Fukaya范畴与正则中心化群方案上的相干层之间的同调镜像对称性，建立了几何兰格lands等价性。

Mirror-reflective algebras and Tachikawa's second conjecture

Given an algebra with an idempotent, we introduce two procedures to construct families of new algebras, termed mirror-reflective algebras and reduced mirror-reflective algebras. We then establish connections among these algebras by recollements of derived module categories. In case of given algebras being gendo-symmetric, we show that the (reduced) mirror-reflective algebras are symmetric and provide new methods to construct systematically both higher dimensional (minimal) Auslander-Gorenstein algebras and gendo-symmetric algebras of higher dominant dimensions. This leads to a new formulation …

镜像反射代数的导出等价

Derived equivalences for mirror-reflective algebras

本文证明镜像反射代数的构造保持 gendo-对称代数的导出等价，即若两个 gendo-对称代数导出等价，则其对应的镜像反射代数也导出等价。

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

In this short note we show that the Bruhat cells in real normal forms of semisimple Lie algebras enjoy the same property as their complex analogs: for any two elements $w$, $w'$ in the Weyl group $W(\mathfrak g)$, the corresponding real Bruhat cell $X_w$ intersects with the dual Bruhat cell $Y_{w'}$ iff $w\prec w'$ in the Bruhat order on $W(\mathfrak g)$. Here $\mathfrak g$ is a normal real form of a semisimple complex Lie algebra $\mathfrak g_\mathbb C$. Our reasoning is based on the properties of the Toda flows rather than on the analysis of the Weyl group action and geometric considerations…