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On the Langlands retraction

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arxiv 1301.1940 v1 pith:LWGEXUAM submitted 2013-01-09 math.RT math.AGmath.CO

Vladimir Drinfeld This is my paper · ORCID
classification math.RTmath.AGmath.CO
keywords langlandsretractionreviewarxivcanonicalcertainchambercoarsening
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Given a root system in a vector space V, Robert Langlands defined in 1973 a canonical retraction of V onto the dominant chamber. In this note we give a short review of the material on this retraction (which is well known under the name of "Langlands' geometric lemmas"). The main purpose of this review is to provide a convenient reference for e-print arXiv:1112.2402 by D.Gaitsgory and me, in which the Langlands retraction is used to define a certain coarsening of the Harder-Narasimhan-Shatz stratification of the stack of G-bundles on a smooth projective curve.

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  1. Langlands Duality and Invariant Differential Operators

    math.RT 2024-11 conditional novelty 4.0 of 10

    The paper connects invariant differential operators to Langlands duality by showing that Knapp-Stein duality in representation multiplets of SL(2n,R) mimics Langlands dual pairs.

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