|
Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)
Cluster Configuration Spaces of Finite Type
Nima Arkani-Hameda, Song Hebcde, Thomas Lamf a School of Natural Sciences, Institute for Advanced Studies, Princeton, NJ, 08540, USA
b CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,
Chinese Academy of Sciences, Beijing, 100190, China
c University of Chinese Academy of Sciences, Beijing
d School of Fundamental Physics and Mathematical Sciences,
Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
e School of Physical Sciences, University of Chinese Academy of Sciences,
No.19A Yuquan Road, Beijing 100049, China
f Department of Mathematics, University of Michigan,
530 Church St, Ann Arbor, MI 48109, USA
Аннотация:
For each Dynkin diagram $D$, we define a “cluster configuration space” ${\mathcal{M}}_D$ and a partial compactification ${\widetilde {\mathcal{M}}}_D$. For $D = A_{n-3}$, we have ${\mathcal{M}}_{A_{n-3}} = {\mathcal{M}}_{0,n}$, the configuration space of $n$ points on ${\mathbb P}^1$, and the partial compactification ${\widetilde {\mathcal{M}}}_{A_{n-3}}$ was studied in this case by Brown. The space ${\widetilde {\mathcal{M}}}_D$ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton–Fomin–Zelevinsky generalized associahedron. The regular functions on ${\widetilde {\mathcal{M}}}_D$ are generated by coordinates $u_\gamma$, in bijection with the cluster variables of type $D$, and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.
Ключевые слова:
configuration space, cluster algebras, generalized associahedron, string amplitudes.
Поступила: 5 января 2021 г.; в окончательном варианте 4 октября 2021 г.; опубликована 16 октября 2021 г.
Образец цитирования:
Nima Arkani-Hamed, Song He, Thomas Lam, “Cluster Configuration Spaces of Finite Type”, SIGMA, 17 (2021), 092, 41 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1774 https://www.mathnet.ru/rus/sigma/v17/p92
|
Статистика просмотров: |
Страница аннотации: | 61 | PDF полного текста: | 16 | Список литературы: | 13 |
|