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Microlocal analysis on wonderful varieties. Regularized traces and global characters
Author(s) -
CupitFoutou Stéphanie,
Parthasarathy Aprameyan,
Ramacher Pablo
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500427
Subject(s) - mathematics , equivariant map , differentiable function , locus (genetics) , pure mathematics , integrable system , vector bundle , algebraic group , algebraic number , algebraic variety , character (mathematics) , algebra over a field , mathematical analysis , geometry , biochemistry , chemistry , gene
Let G be a connected reductive complex algebraic group with split real form ( G , σ ) . Consider a strict wonderful G ‐variety X equipped with its σ‐equivariant real structure, and let X be the corresponding real locus. Further, let E be a real differentiable G ‐vector bundle over X . In this paper, we introduce a distribution character for the regular representation of G on the space of smooth sections of E given in terms of the spherical roots of X , and show that on a certain open subset of G of transversal elements it is locally integrable and given by a sum over fixed points.