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:
- Beilinson-Drinfeld, Quantization of Hitchin's Integrable System and Hecke Eigensheaves, section 7.9. Available on line (e.g., Dennis Gaitsgory's web page)
- 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.