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I hope this question is not too unspecific:

Can Soergel's Categorical Local Langlands conjectures [1] be interpreted as special form of geometric Langlands.

I think this is somehow hidden in the work Nadler and Benzvi ([2] for example), however i would like to know if there is direct way to see such a connection.

[1] Soergel, Wolfgang; Langlands' Philosophy and Koszul Duality , Proceedings of NATO ASI 2000 in Constanta, Algebra-Representation Theory, Roggenkamp and Stefanescu (eds.), Kluwer 2001

[2] Benzvi, David; Nadler, David; Loop Spaces and Langlands Parameters arXiv:0706.0322

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    $\begingroup$ Could you tell us what the conjectures are? $\endgroup$
    – S. Carnahan ♦
    Commented Apr 12, 2013 at 11:02
  • $\begingroup$ Yes, at least roughly: Soergel conjectures that the category of smooth admissible representations of a real reductive group $G$ can be described by the equivariant derived category of the so-called Adams-Barbasch-Vogan parameter space (equivariant with respect to some action of the Langlands-dual group of the complexification of $G$) Ok, this has nothing to do with geometric Langlands on first sight, but he also mentions that similar conjectures should hold in the $l$-adic case. $\endgroup$
    – Oliver Straser
    Commented Apr 12, 2013 at 11:46

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