Harish-Chandra pairs and their use in localization is discussed in Beilinson-Bernstein A proof of Jantzen Conjectures, available on Joseph Bernstein's web page. See in particular sections 1.8 and 3.3.

Other sources:

1. Beilinson-Drinfeld, Quantization of Hitchin's Integrable System and Hecke Eigensheaves, section 7.9. Available on line (e.g., Dennis Gaitsgory's web page)
2. Beilinson-Feigin-Mazur Notes on Conformal Field Theory (Incomplete). The discussion is centered around groupoids and the Virasoro algebra. This is on Barry Mazur's web page.

Harish-Chandra pairs and their use in localization is discussed in Beilinson-Bernstein A proof of Jantzen Conjectures, available on Joseph Bernstein's web page. See in particular sections 1.8 and 3.3.

Other sources:

1. Beilinson-Drinfeld, Quantization of Hitchin's Integrable System and Hecke Eigensheaves, sections 7.7-7.9. Available on line.
2. Beilinson-Feigin-Mazur Notes on Conformal Field Theory (Incomplete). The discussion is centered around groupoids and the Virasoro algebra. This is on Barry Mazur's web page (link on the side to "older material").