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?
A formula for the Kac-Weyl character of loop group representations.
(Pressley-Segal 88 (14.3.4), Ando 00, 11.4, Ganter 12, corollary 8.6)
Originally due to Victor Kac.
Andrew Pressley, Graeme Segal, Loop groups Oxford University Press (1988)
Matthew Ando, Power operations in elliptic cohomology and representations of loop groups, Trans. Amer. Math. Soc., 352(12):5619–
5666, 2000 (pdf)
Derivation from fiber integration in equivariant elliptic cohomology is in
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