Complex sentence: Lusztig-Vogan polynomials, introduced in Lusztig and Vogan (1983), are analogous to Kazhdan-Lusztig polynomials, but are tailored to representations of "real" semisimple Lie groups, and play major role in the conjectural description of their unitary duals.
Split into simpler sentences: Lusztig-Vogan polynomials (also called Kazhdan-Lusztig polynomials or Kazhdan-Lusztig-Vogan polynomials) were introduced in Lusztig and Vogan (1983). They are analogous to Kazhdan-Lusztig polynomials, but are tailored to representations of "real" semisimple Lie groups, and play major role in the conjectural description of their unitary duals.