Эта публикация цитируется в
14 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.
MSC: 05E14,
13F60,
14N99,
81T30 Поступила: 5 января 2021 г.; в окончательном варианте
4 октября 2021 г.; опубликована
16 октября 2021 г.
Язык публикации: английский
DOI:
10.3842/SIGMA.2021.092