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?
Consider a complex reductive group with Lie algebra , Borel subgroup , and flag variety . The localization theory of Beilinson-Bernstein identifies representations of with global sections of (twisted) D-modules on . In particular, highest weight representations are realized by -equivariant -modules on , or in other words, by -modules on the quotient stack .
Furthermore, given a subgroup , it identifies modules for the Harish-Chandra pair? with global sections of -equivariant twisted -modules on .
The case gives the Borel-Weil description of irreducible algebraic (equivalently, finite-dimensional) representations of as sections of equivariant line bundles on .
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Hendrik Orem, Lecture notes: The Beilinson-Bernstein Localization Theorem, pdf
David Ben-Zvi, David Nadler, Loop Spaces and Langlands Parameters (arXiv:0706.0322))
Last revised on November 30, 2018 at 08:41:26. See the history of this page for a list of all contributions to it.