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Title: The partial compactification of the universal centralizer
The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise compactification of the universal centralizer by taking the closure of each fiber in the wonderful compactification. We use the geometry of the wonderful compactification to give an explicit description of the symplectic leaves of this new space. We also show that its compactified centralizer fibers are isomorphic to certain Hessenberg varieties—we apply this connection to compute the singular cohomology of the compactification, and to study the geometry of the corresponding universal Hessenberg family.  more » « less
Award ID(s):
1902921
PAR ID:
10479048
Author(s) / Creator(s):
Publisher / Repository:
Springer
Date Published:
Journal Name:
Selecta Mathematica
Volume:
29
Issue:
5
ISSN:
1022-1824
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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