Langlands duality for Hitchin systems TeX Export

@misc{citeulike:612190, abstract = {We show that the Hitchin integrable system for a simple complex Lie group \$G\$ is dual to the Hitchin system for the Langlands dual group \$\lan{G}\$. In particular, the general fiber of the connected component \$\Higgs\_0\$ of the Hitchin system for \$G\$ is an abelian variety which is dual to the corresponding fiber of the connected component of the Hitchin system for \$\lan{G}\$. The non-neutral connected components \$\Higgs\_{\alpha}\$ form torsors over \$\Higgs\_0\$. We show that their duals are gerbes over \$\Higgs\_0\$ which are induced by the gerbe of \$G\$-Higgs bundles \$\gHiggs\$. More generally, we establish a duality between the gerbe \$\gHiggs\$ of \$G\$-Higgs bundles and the gerbe \$\lan{\gHiggs}\$ of \$\lan{G}\$-Higgs bundles, which incorporates all the previous dualities. All these results extend immediately to an arbirtary connected complex reductive group \$\mathbb{G}\$.}, archivePrefix = {arXiv}, author = {Donagi, Ron and Pantev, Tony}, citeulike-article-id = {612190}, citeulike-linkout-0 = {http://arxiv.org/abs/math.AG/0604617}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.AG/0604617}, day = {29}, eprint = {math.AG/0604617}, keywords = {duality, group, hitchin, langlands, lie}, month = {Apr}, posted-at = {2006-05-03 13:01:32}, priority = {2}, title = {Langlands duality for Hitchin systems}, url = {http://arxiv.org/abs/math.AG/0604617}, year = {2006} }

TY - ELEC ID - citeulike:612190 L3 - citeulike-article-id:612190 N2 - We show that the Hitchin integrable system for a simple complex Lie group $G$ is dual to the Hitchin system for the Langlands dual group $\lan{G}$. In particular, the general fiber of the connected component $\Higgs_0$ of the Hitchin system for $G$ is an abelian variety which is dual to the corresponding fiber of the connected component of the Hitchin system for $\lan{G}$. The non-neutral connected components $\Higgs_{\alpha}$ form torsors over $\Higgs_0$. We show that their duals are gerbes over $\Higgs_0$ which are induced by the gerbe of $G$-Higgs bundles $\gHiggs$. More generally, we establish a duality between the gerbe $\gHiggs$ of $G$-Higgs bundles and the gerbe $\lan{\gHiggs}$ of $\lan{G}$-Higgs bundles, which incorporates all the previous dualities. All these results extend immediately to an arbirtary connected complex reductive group $\mathbb{G}$. TI - Langlands duality for Hitchin systems KW - duality KW - group KW - hitchin KW - langlands KW - lie AU - Donagi, Ron AU - Pantev, Tony PY - 2006/Apr/29/ UR - http://arxiv.org/abs/math.AG/0604617 ER -