Results 1 to 10 of about 53 (35)
PRESENTATIONS OF AFFINE KAC–MOODY GROUPS [PDF]
Forum of Mathematics, Sigma, 2018 How many generators and relations does $\text{SL}\,_{n}(\mathbb{F}_{q}[t,t^{-1}])$ need? In this paper we exhibit its explicit presentation with $9$ generators and $44$ relations. We investigate presentations of affine Kac–Moody groups over finite fields.
INNA CAPDEBOSCQ +2 more
doaj +4 more sources
Frobenius splitting of Schubert varieties of semi-infinite flag manifolds
Forum of Mathematics, Pi, 2021 We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field ${\mathbb K}$ of characteristic $\neq 2$ from scratch.
Syu Kato
doaj +1 more source
Grassmanniennes affines tordues sur les entiers
Forum of Mathematics, Sigma, 2023 We generalize the works of Pappas–Rapoport–Zhu on twisted affine Grassmannians to the wildly ramified case under mild assumptions. This rests on a construction of certain smooth affine $\mathbb {Z}[t]$ -groups with connected fibers of parahoric ...
João Lourenço
doaj +1 more source
Kac-Moody Groups and Completions [PDF]
, 2020 In this paper we construct a new "pro-p-complete" topological Kac-Moody group and compare it to various known topological Kac-Moody groups. We come across this group by investigating the process of completion of groups with BN-pairs.
Capdeboscq, Inna, Rumynin, Dmitriy
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On some pro-p groups from infinite-dimensional Lie theory [PDF]
, 2013 We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite fields, with respect to various completions of algebraic or geometric ...
Capdeboscq, Inna, Remy, Bertrand
core +4 more sources
No repulsion between critical points for planar Gaussian random fields [PDF]
, 2020 We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal.
Belyaev, Dmitry +2 more
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Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations [PDF]
, 2023 We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations. As a consequence, we show that the affine Kac-Moody group of type X(r) N is
Morita, Jun +2 more
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Presentations: from Kac-Moody groups to profinite and back [PDF]
, 2015 We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on ...
A Devillers +20 more
core +3 more sources
Hyperbolic generalized triangle groups, property (T) and finite simple quotients [PDF]
, 2021 We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan\u27s property (T). Some of them are significantly shorter than the previously known shortest examples.
Caprace, Pierre-Emmanuel +3 more
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Kac-Moody Groups and Cosheaves on Davis Building [PDF]
, 2018 We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building.
Hristova, Katerina, Rumynin, Dmitriy
core +2 more sources