most recent 30 from http://mathoverflow.net 2013-05-22T22:56:19Z http://mathoverflow.net/feeds/user/4013 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/1972/langlands-dual-groups/15362#15362 David Vogan 2010-02-15T20:53:24Z 2010-02-15T20:53:24Z

<p>The Chevalley construction mentioned by Steven Sam from Lusztig's notes can also be found in Springer's textbook "Linear algebraic groups" (on pages 164-165 of the second edition). It's beautiful and clear and elementary (no perverse sheaves!) and direct (no Lie algebras, which wouldn't work in finite characteristic, and no reduction to simply connected groups). If you want to construct representations of the dual group directly, then geometric Satake is a good idea. For the classical Langlands conjectures, what one cares about are not representations of the dual group but elements of it (or a little more precisely, maps of Galois groups into it). For such purposes, the Chevalley construction by generators and relations is just what Dr. Langlands ordered.</p>