geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
A kind of module/representation over a pair consisting of a semisimple Lie algebra and an algebraic group.
wikipedia: (g,K)-module, Harish-Chandra module
David Vogan, Jr., Unitary Representations of Reductive Lie Groups, Annals of Mathematics Studies 118, Princeton Univ. Press 1987
A. W. Knapp, D. A. Vogan, Cohomological induction and unitary representations, Princeton Univ. Press, 1995.
Harish-Chandra, Representations of semi-simple lie groups I, Trans. Amer. Math. Soc. 75, 185–243, 1953; II, Trans. AMS 76, 26–65, 1954; III, Trans. AMS 76, 245–253, 1954.
Fabian Januszewski, Algebraic characters for Harish-Chandra modules, arxiv/1201.2447