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- W2254239372 abstract "Let G be a rank 2 complete affine or hyperbolic simply-connected Kac–Moody group over a finite field k. Then G is locally compact and totally disconnected. Let B− = HU− be the negative minimal parabolic subgroup of G, where H is the analog of a diagonal subgroup and U− is generated by all negative real root groups. Let w1 and w2 be the generators of the Weyl group. Let be the negative standard parabolic subgroup of G corresponding to w1. It is known that the subgroups U−, B− and , are nonuniform lattice subgroups of G. Here we construct an infinite sequence of congruence subgroups of as natural generalizations of the corresponding notions for lattices in Lie groups. We also show that the group U− contains analogous congruence subgroups. Our technique involves determining graphs of groups presentations for U−, B−, and with the fundamental apartment of the Bruhat–Tits tree X a quotient graph for U− and for B− on X. When k = 𝔽q and q = 2s, the graph of groups for has the the positive half of the fundamental ..." @default.
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- W2254239372 date "2016-01-29" @default.
- W2254239372 modified "2023-10-17" @default.
- W2254239372 title "Congruence Subgroups of Lattices in Rank 2 Kac–Moody Groups over Finite Fields" @default.
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- W2254239372 doi "https://doi.org/10.1080/00927872.2015.1012673" @default.
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