图 书 馆
“巧合”反射群的组合学Combinatorics of the "coincidental" reflection groups |
|
| 课程网址: | http://videolectures.net/FPSAC2019_williams_reflection_groups/ |
| 主讲教师: | Vic Reiner |
| 开课单位: | 明尼苏达大学 |
| 开课时间: | 2019-07-19 |
| 课程语种: | 英语 |
| 中文简介: |  许多现代组合数学都涉及有限反射群，包括实数和复数。神秘的是，许多结果对于所谓的“巧合”反射组特别有效。这些是在 n 维空间中由 n 个反射产生的群，它们的指数形成一个等差数列——它们是类型 A、B/C、H3、二面体群和所有非实 Shephard 群（规则的对称性复杂的多胞体）。本次演讲将讨论以巧合群体为特色的近期工作。这包括最近与 Shepler 和 Sommers 合作的工作，揭示了他们特别优雅的不变理论，从而得出了其相关簇复合体的面数和 h 向量的乘积公式，以及将 h 向量转换为 f 向量的 q 类似物。我们还希望讨论其他人的定理和猜想，例如 Alex Miller、Barnard-Reading、Hamaker-Patrias-Pechenik-Williams 和 Sam Hopkins。 |
| 课程简介: | Much modern combinatorics involves finite reflection groups, both real and complex. Mysteriously, many results work particularly well for the so-called "coincidental" reflection groups. These are the groups generated by n reflections acting in n-dimensional space whose exponents form an arithmetic sequence – they are the real reflection groups of types A, B/C, H3, dihedral groups, and all non-real Shephard groups (the symmetries of regular complex polytopes). This talk will discuss recent work featuring the coincidental groups. This includes recent work with Shepler and Sommers uncovering their extra elegant invariant theory, leading to product formulas for the face numbers and h-vectors of their associated cluster complexes, and a q-analogue of the transformation taking the h-vector to f-vector. We also hope to discuss theorems and conjectures of various others, such as Alex Miller, Barnard–Reading, Hamaker–Patrias–Pechenik–Williams, and Sam Hopkins. |
| 关 键 词: | 有限反射群; 二面体群; 多胞体 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-06-04：yumf |
| 最后编审: | 2021-06-04：yumf |
| 阅读次数: | 74 |