What is an Oper? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T08:46:44Z http://mathoverflow.net/feeds/question/2503 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/2503/what-is-an-oper What is an Oper? Charles Siegel 2009-10-25T19:39:51Z 2009-10-26T04:17:12Z <p>Given a curve C, and a reductive group G, there is a moduli stack Loc_G(C), the stack of G-local systems. I keep reading that there's a substack of "opers" but am having trouble locating a definition. So what's an oper, and how should I think about them?</p> http://mathoverflow.net/questions/2503/what-is-an-oper/2535#2535 Answer by Tony Pantev for What is an Oper? Tony Pantev 2009-10-25T23:52:25Z 2009-10-25T23:52:25Z <p>Look at <a href="http://arxiv.org/abs/math/0501398" rel="nofollow">http://arxiv.org/abs/math/0501398</a>.</p> http://mathoverflow.net/questions/2503/what-is-an-oper/2552#2552 Answer by Mike Skirvin for What is an Oper? Mike Skirvin 2009-10-26T04:17:12Z 2009-10-26T04:17:12Z <p>Edward Frenkel also has a number of papers which deal with opers (just look at his arxiv papers for example). In particular, I'm fond of the paper he wrote with David Ben-Zvi <a href="http://arxiv.org/abs/math/9902068" rel="nofollow">http://arxiv.org/abs/math/9902068</a></p> <p>I think this paper might be of particular interest to Charles given that I've seen him previously give links to the BNR paper. This paper by Frenkel and Ben-Zvi relates spectral curves to opers and also gives some nice historical background on how each is related to solving certain kinds of differential equations (which is the kind of thing I'm glad to know is there, even if I don't study it that way).</p>