Critical values of moment maps on quantizable manifolds
| dc.creator | Viña, Andrés | |
| dc.date | 2007-11-02 | |
| dc.date.accessioned | 2026-07-07T08:40:15Z | |
| dc.date.available | 2026-07-07T08:40:15Z | |
| dc.description | Let $M$ be a quantizable symplectic manifold acted on by $T=(S^1)^r$ in a Hamiltonian fashion and $J$ a moment map for this action. Suppose that the set $M^{T}$ of fixed points is discrete and denote by $α_{pj}\in{\mathbb Z}^r$ the weights of the isotropy representation at $p$. By means of the $α_{pj}$'s we define a partition ${\mathcal Q}_+$, ${\mathcal Q}_-$ of $M^T$. (When $r=1$, ${\mathcal Q}_{\pm}$ will be the set of fixed points such that the half of the Morse index of $J$ at them is even (odd)). We prove the existence of a map $π_{\pm}:{\mathcal Q}_{\pm}\to{\mathcal Q}_{\mp}$ such that $J(q)-J(π_{\pm}(q))\in I_{\mp}$, for all $q\in {\mathcal Q}_{\pm}$, where $I_{\pm}$ is the lattice generated by the $α_{pj}$'s with $p\in{\mathcal Q}_{\pm}.$ We define partition functions $N_p$ similar to the ones of Kostant \cite{Gui} and we prove that $\sum_{p\in{\mathcal Q}_+}N_p(l)=\sum_{p\in{\mathcal Q}_-}N_p(l)$, for any $l\in{\mathbb Z}^r$ with $|l|$ sufficiently large. | |
| dc.description | 10 pages, comments are wellcome | |
| dc.identifier | https://arxiv.org/abs/0711.0358 | |
| dc.identifier | http://arxiv.org/abs/0711.0358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141322 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D20; 58J20 | |
| dc.title | Critical values of moment maps on quantizable manifolds | |
| dc.type | text |