PRESENTATIONS: FROM KAC-MOODY GROUPS TO PROFINITE AND BACK
نویسندگان
چکیده
منابع مشابه
Lattices in Kac - Moody Groups
Initially, we set out to construct non-uniform ‘arithmetic’ lattices in Kac-Moody groups of rank 2 over finite fields, as constructed by Tits ([Ti1], [Ti2]) using the BruhatTits tree of a Tits system for such groups. This attempt succeeded, and in fact, the construction we used can be applied to higher rank Kac-Moody groups over sufficiently large finite fields, and their buildings (Theorem 1.7...
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We give the definition of a kind of building I for a symmetrizable KacMoody group over a field K endowed with a dicrete valuation and with a residue field containing C. Due to some bad properties, we call this I a hovel. Nevertheless I has some good properties, for example the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semi-simpl...
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The proposed project is set in pure mathematics within the areas of infinite-dimensional Lie theory and geometric group theory. Its goal is to contribute to the structure theory of unitary forms (i.e., centralisers of Chevalley involutions) of Kac–Moody algebras and of Kac–Moody groups of indefinite type. The main emphasis of this project will be on finite-dimensional representations and on ide...
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The Iwasawa decomposition of a connected semisimple complex Lie group or a connected semisimple split real Lie group is one of the most fundamental observations of classical Lie theory. It implies that the geometry of a connected semisimple complex resp. split real Lie group G is controlled by any maximal compact subgroup K. Examples are Weyl’s unitarian trick in the representation theory of Li...
متن کاملAbstract involutions of algebraic groups and of Kac–Moody groups
Based on the second author’s thesis [Hor08] 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 [Spr84], [HW93] for algebraic groups and in [KW92] for certain Kac–Moody gro...
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ژورنال
عنوان ژورنال: Transformation Groups
سال: 2016
ISSN: 1083-4362,1531-586X
DOI: 10.1007/s00031-016-9411-8