Parameterization of factorizable line bundles by K-theory and motivic cohomology
Dennis Gaitsgory
TL;DR
This paper revises a previous construction linking Brylinski-Deligne data to factorization line bundles on the affine Grassmannian, clarifying the relationship with K-theory and motivic cohomology.
Contribution
It corrects and refines the construction of factorization line bundles from Brylinski-Deligne data, emphasizing the role of K-theory and motivic cohomology.
Findings
Corrected the previous construction for accuracy.
Clarified the connection between Brylinski-Deligne data and line bundles.
Enhanced understanding of the role of K-theory in geometric representation theory.
Abstract
This note corrects a certain construction in (the old version of) the paper [GL]. The construction in question starts from a Brylinski-Deligne datum, which is an extension of a group G by K_2, and produces a factorization line bundle on the affine Grassmannian of the group G.
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