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
Be?linson-Bernstein localization?
Asymptotic representation theory is representation theory in the limit of large dimension of linear representation and/or of large groups being represented.
Much of asymptotic representation theory is concerned specifically with the symmetric group and studies asymptotics of shapes of Young diagrams and of numbers of Young tableaux under measures such as the Plancherel measure and/or the Schur-Weyl measure.
Anatoly Vershik, Two lectures on the asymptotic representation theory and statistics of Young diagrams, In: Vershik A.M., Yakubovich Y. (eds) Asymptotic Combinatorics with Applications to Mathematical Physics Lecture Notes in Mathematics, vol 1815. Springer 2003 (doi:10.1007/3-540-44890-X_7)
G. Olshanski, Asymptotic representation theory, Lecture notes 2009-2010 (webpage, pdf 1, pdf 2)
Piotr Śniady, Combinatorics of asymptotic representation theory, European Congress of Mathematics 2012 (arXiv:1203.6509)
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