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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Burness, T.C.

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Volume 14, Issue 2


Abstract involutions of algebraic groups and of Kac–Moody groups

Ralf Gramlich
  • Fachbereich Mathematik, TU Darmstadt, Schloßgartenstr. 7, 64289 Darmstadt, Germany and School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom
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/ Max Horn / Bernhard Mühlherr
Published Online: 2010-07-21 | DOI: https://doi.org/10.1515/jgt.2010.033


Based on the second author's thesis [Horn, Involutions of Kac–Moody groups, TU Darmstadt, 2008], in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac–Moody groups using twin buildings, RGD systems, and twisted involutions of Coxeter groups. Notably we simultaneously generalize the double coset decompositions established in [Helminck, Wang, Adv. Math. 99: 26–96, 1993] and [Springer, Algebraic groups and related topics: 525–543, North-Holland, 1984] for algebraic groups and in [Kac, Wang, Adv. Math. 92: 129–195, 1992] for certain Kac–Moody groups, we analyze the filtration studied in [Devillers, Mühlherr, Forum Math. 19: 955–970, 2007] in the context of arbitrary involutions, and we answer a structural question on the combinatorics of involutions of twin buildings raised in [Bennett, Gramlich, Hoffman, Shpectorov, Curtis–Phan–Tits theory: 13–29, World Scientific, 2003].

About the article

Received: 2009-08-11

Revised: 2010-03-30

Published Online: 2010-07-21

Published in Print: 2011-04-01

Citation Information: Journal of Group Theory, Volume 14, Issue 2, Pages 213–249, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2010.033.

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