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Differential equations and Lie group representations
We discuss the role of differential equations in Lie group representation theory. We use Kashiwara’s pentagon as a reference frame for the real...
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Nilpotent Orbits of Orthogonal Groups over p-adic Fields, and the DeBacker Parametrization
For local non-archimedean fields k of sufficiently large residual characteristic, we explicitly parametrize and count the rational nilpotent adjoint...
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Deligne–Lusztig duality and wonderful compactification
We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne–Lusztig (or Alvis–Curtis) duality for p -adic...
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Arithmetic Levi–Cività connection
This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic...
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The algebraisation of higher Deligne–Lusztig representations
In this paper we study higher Deligne–Lusztig representations of reductive groups over finite quotients of discrete valuation rings. At even levels,...
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On p-adic Colligations and ‘Rational Maps’ of Bruhat–Tits Trees
Consider matrices of order k+N over p-adic field determined up to conjugations by elements of GL(N) over p-adic integers. We define a product of such...
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Stratifications in the reduction of Shimura varieties
In the paper four stratifications in the reduction modulo p of a general Shimura variety are studied: the Newton stratification, the...
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Strongly concave functions on root systems
Let F be a local complete field with discrete valuation, and let G be the group of F -points of a quasisplit group over F . Let ℬ be the Bruhat-Tits...
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Deformation of proper actions on reductive homogeneous spaces
Let G be a real reductive Lie group and H a closed reductive subgroup of G . We investigate the deformation of standard compact quotients of G / H , that...
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A tropical view on Bruhat-Tits buildings and their compactifications
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable...
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On p-adic norms and quadratic extensions, II
We investigate the graph theoretical aspects and combinatorics of the action of a unitary group in n variables over a local non-archimedian field on...
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Affine Springer Fibers and Affine Deligne-Lusztig Varieties
We give a survey on the notion of affine Grassmannian, on affine Springer fibers and the purity conjecture of Goresky, Kottwitz, and MacPherson, and...
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On Nilpotent Orbits of SL n and Sp2n over a Local Non-Archimedean Field
We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the classical groups SL n and Sp 2 n ...
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The Iwasava decomposition and intermediate subgroups of the Steinberg groups over the field of fractions of a principal ideal ring
Abstract The Iwasava decomposition is proved for the Steinberg groups of types 2 A 2 l −1 , 2 D l , 2 E 6 , 3 D 4 over the field of fractions of a...