The centralizers of root subgroups in KacMoody Steinberg groups
Abstract
For the affine and hyperbolic root system the symmetric part of the centralizers of root subgroups in the corresponding Steinberg groups are calculated. In the affine case the corresponding root subsystems can be computed in term of the centralizers in the spherical root systems, while in the hyperbolic case there emerges a "zoo" of examples, many of them nonhyperbolic. This also delivers many examples of naturally occuring root subsystems of infinite rank.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.06731
 Bibcode:
 2021arXiv210806731S
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Group Theory
 EPrint:
 40 pages, 2 figures, 4 tables, innumerable diagrams