In the field of mathematics known as representation theory, an L-packet is a collection of (isomorphism classes of) irreducible representations of a reductive group over a local field, that are L-indistinguishable, meaning they have the same Langlands parameter, and so have the same L-function and ε-factors.
The L-packets, and therefore the irreducible representations, correspond to quasicharacters of a Cartan subgroup, up to conjugacy under the Weyl group.
For general linear groups over local fields, the L-packets have just one representation in them (up to isomorphism).
For example, the discrete series representations of SL2(R) are grouped into L-packets with two elements.
On the other hand, the centralizer of a subset of the projective general linear group can have more than 1 component, corresponding to the fact that L-packets for the special linear group can have more than 1 element.