The Langlands dual group of a connected reductive group is the reductive group whose root datum
is obtained by interchanging roots with coroots and characters with cocharacters.
It is usually taken over a characteristic-zero
coefficient field and denoted 
or 
. For example, the dual of 
is 
, while 
is self-dual. This duality
concerns the root datum, rather than a dual vector space.
Arthur parameters take values in the dual group, and a Hecke eigensheaf has an eigenvalue given by a local system for that group.
