A generalization of a theorem of Minkowski
A note on the arithmetic of the orthogonal group - II
À propos d’un lemme de Ribet
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 non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation...
Addendum : Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups
Algèbres de Hecke et induites de représentations cuspidales, pour GL (N).
Barnes' identities and representations of GL (2). II. Nonarchimedian local field case.
Base change for Bernstein centers of depth zero principal series blocks
Let be an unramified group over a -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with -level structure initiated by M. Rapoport and the author in [15].
Combinatorial and group-theoretic compactifications of buildings
Let be a building of arbitrary type. A compactification of the set of spherical residues of is introduced. We prove that it coincides with the horofunction compactification of endowed with a natural combinatorial distance which we call the root-distance. Points of admit amenable stabilisers in and conversely, any amenable subgroup virtually fixes a point in . In addition, it is shown that, provided is transitive enough, this compactification also coincides with the group-theoretic...
Compactification of the Bruhat-Tits building of PGL by lattices of smaller rank.
Compléments à l'article «Groupes réductifs»
Continuous Cohomology and p-Adic Galois Representations.
Counting arithmetic subgroups and subgroup growth of virtually free groups
Let be a -adic field, and let endowed with the Haar measure determined by giving a maximal compact subgroup measure . Let denote the number of conjugacy classes of arithmetic lattices in with co-volume bounded by . We show that under the assumption that does not contain the element , where denotes the -th root of unity over , we have where denotes the order of the residue field of .
Darstellungen von SL(2,.../p...) und Thetafunktionen. II.
Degree two monomial representations of local Weil groups.
Die irreduziblen Darstellungen der Gruppen SL...(Z...), insbesondere SL...(Z...). II. Teil
Die irreduziblen Darstellungen der Gruppen SL...(Z...), insbesondere SL...(Z...). I. Teil
Dimensions of some affine Deligne–Lusztig varieties
Dual Blobs and Plancherel Formulas
Let be a -adic field. Let be the group of -rational points of a connected reductive group defined over , and let be its Lie algebra. Under certain hypotheses on and , wequantifythe tempered dual of via the Plancherel formula on , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on and . As a consequence, we prove that any tempered representation contains a good minimal -type; we extend this result to irreducible...
Dual pair G... x PGL2 G... is the automorphism group of the Jordan algebra.