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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 10th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated _[[conjugacy class]]_

   created conjugacy class

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI don't have time to edit things now, but the example is wrong.

   I don’t have time to edit things now, but the example is wrong.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexSorry. Fixed. Thanks.

   Sorry. Fixed. Thanks.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexWas that a coincidence you started this entry on the same day as I wrote [this](http://golem.ph.utexas.edu/category/2010/08/what_is_the_langlands_programm.html#c041786)? What David Ben-Zvi says above seems worth including. Something like >For any finite group the number of its conjugacy classes is equal to the number of its irreducible representations. For finite groups of Lie type this result can be strengthened to show that there is a canonical way to match conjugacy classes of a group $G$ to the irreducible representations of its Langlands dual $G'$.

   Was that a coincidence you started this entry on the same day as I wrote this?

   What David Ben-Zvi says above seems worth including. Something like

   For any finite group the number of its conjugacy classes is equal to the number of its irreducible representations. For finite groups of Lie type this result can be strengthened to show that there is a canonical way to match conjugacy classes of a group $G$ to the irreducible representations of its Langlands dual $G'$.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItex> seems worth including Please do!

   seems worth including

   Please do!

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexOK, though I'm nervous about Ben-Zvi's >I won’t give the precise statement but I think this is not a particularly misleading simplification Anyway, doing that had me then create [[group of Lie type]].

   OK, though I’m nervous about Ben-Zvi’s

   I won’t give the precise statement but I think this is not a particularly misleading simplification

   Anyway, doing that had me then create group of Lie type.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItex> OK, though I'm nervous Just add a corresponding disclaimer, making it clear that what you say is meant as a helpful guiding idea, not as a precise statement.

   OK, though I’m nervous

   Just add a corresponding disclaimer, making it clear that what you say is meant as a helpful guiding idea, not as a precise statement.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItex> doing that had me then create [[group of Lie type]]. Thanks. I have added a warning and links, and linked to it from _[[group]]_.

   doing that had me then create group of Lie type.

   Thanks. I have added a warning and links, and linked to it from group.

9. • CommentRowNumber9.
   • CommentAuthorzskoda
   • CommentTimeJul 11th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWikipedia is here useful, esp. for terminology: [group of Lie type](http://en.wikipedia.org/wiki/Group_of_Lie_type).

   Wikipedia is here useful, esp. for terminology: group of Lie type.