Cocompact lattices in locally pro-$p$-complete rank-2 Kac-Moody groups
نویسندگان
چکیده
منابع مشابه
Lattices in Complete Rank 2 Kac–moody Groups
Let Λ be a minimal Kac–Moody group of rank 2 defined over the finite field Fq , where q = pa with p prime. Let G be the topological Kac–Moody group obtained by completing Λ. An example is G = SL2(K), where K is the field of formal Laurent series over Fq . The group G acts on its Bruhat–Tits building X, a tree, with quotient a single edge. We construct new examples of cocompact lattices in G, ma...
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Let G be a complete Kac–Moody group of rank n ≥ 2 such that the Weyl group of G is a free product of cyclic groups of order 2. We construct new families of examples of cocompact lattices in G, many of which act transitively on the chambers of the building for G.
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Let G be a topological Kac–Moody group of rank 2 with symmetric Cartan matrix, defined over a finite field Fq . An example is G = SL(2,Fq((t−1))). We determine a positive lower bound on the covolumes of cocompact lattices in G, and construct a cocompact lattice Γ0 < G which realises this minimum. This completes the work begun in Part I, which considered the cases when G admits an edge-transitiv...
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Let A be a symmetrizable affine or hyperbolic generalized Cartan matrix. Let G be a locally compact Kac-Moody group associated to A over a finite field Fq. We suppose that G has type ∞, that is, the Weyl group W of G is a free product of Z/2Z’s. This includes all locally compact Kac-Moody groups of rank 2 and three possible locally compact rank 3 Kac-Moody groups of noncompact hyperbolic type. ...
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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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ژورنال
عنوان ژورنال: Sbornik: Mathematics
سال: 2020
ISSN: 1064-5616,1468-4802
DOI: 10.1070/sm9311