Here is a proposition:
Let $\pi$ be an irreducible unitary representation of $GL_2(\mathbb{R})$. It can be realized as a component of the induced representation from a character $(\chi_1,\chi_2)$ on the Borel group $B$. If $\pi$ is not square-integrable then it is a Langlands quotient $\chi_1 \boxplus \chi_2$. The central character is $\chi_1 \chi_2$.
My question is: What is the meaning of 'Langlands quotient ' here? Thanks a lot!