Affine Deligne-Lusztig varieties in affine flag varieties

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.Comment: 44 pages, 4 figures. Minor changes to font, references, and acknowledgments. Improved introduction, other improvements in exposition, and two new figures added, for a total of

Dimensions of some affine Deligne-Lusztig varieties

This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties X_mu(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of superbasic b. In the affine flag manifold, we prove a formula that reduces the dimension question for X_x(b) with b in the split torus to computations of dimensions of intersections of Iwahori orbits with orbits of the unipotent radical. Calculations using this formula allow us to verify a conjecture of Reuman in many new cases, and to make progress toward a generalization of his conjecture.Comment: 51 pages, 12 figure

On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Hydraulic Characteristics of Rills

Rill density and rill flow rates were determined during rainfall simulation tests conducted at 11 sites located throughout the eastern United States. A mean rill density of 1.0 rills/m was found for the study locations. From measurements of the relative distribution of flow rates, a procedure is identified for partitioning flow between individual rills. Regression equations were developed for relating rill width and hydraulic roughness coefficients to flow rate. Equations were also derived for predicting mean flow velocity from visually determined measurements of advance velocity. Information reported in this study can be used to estimate hydraulic characteristics of rills

Iwahori-Hecke algebras

Our aim here is to give a fairly self-contained exposition of some basic facts about the Iwahori-Hecke algebra H of a split p-adic group, including Bernstein's presentation and description of the center, Macdonald's formula, the CasselmanShalika formula, and the Kato-Lusztig formula. There are no new results here, and the same is essentially true of the proofs. We have been strongly influenced by the notes [1] of a course given by Bernstein. The reader may find in The following notation will be used throughout this paper. We work over a padic field F with valuation ring O and prime ideal P = (π). We denote by k the residue field O/P and by q the cardinality of k. Consider a split connected reductive group G over F , with split maximal torus A and Borel subgroup B = AN containing A. We writeB = AN for the Borel subgroup containing A that is opposite to B. We assume that G, A, N are defined over O. We write K for G(O) an

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Dystonia Type 6 Gene Product Thap1: Identification Of a 50 kDa DNA-binding Species In Neuronal Nuclear Fractions

Mutations in THAP1 result in dystonia type 6, with partial penetrance and variable phenotype. The goal of this study was to examine the nature and expression pattern of the protein product(s) of the Thap1 transcription factor (DYT6 gene) in mouse neurons, and to study the regional and developmental distribution, and subcellular localization of Thap1 protein. The goal was accomplished via overexpression and knock-down of Thap1 in the HEK293T cell line and in mouse striatal primary cultures and western blotting of embryonic Thap1-null tissue. The endogenous and transduced Thap1 isoforms were characterized using three different commercially available anti-Thap1 antibodies and validated by immunoprecipitation and DNA oligonucleotide affinity chromatography. We identified multiple, novel Thap1 species of apparent Mr 32 kDa, 47 kDa, and 50–52 kDa in vitro and in vivo, and verified the previously identified species at 29–30 kDa in neurons. The Thap1 species at the 50 kDa size range was exclusively detected in murine brain and testes and were located in the nuclear compartment. Thus, in addition to the predicted 25 kDa apparent Mr, we identified Thap1 species with greater apparent Mr that we speculate may be a result of posttranslational modifications. The neural localization of the 50 kDa species and its nuclear compartmentalization suggests that these may be key Thap1 species controlling neuronal gene transcription. Dysfunction of the neuronal 50 kDa species may therefore be implicated in the pathogenesis of DYT6

A Prospective Pilot Study to Identify a Myocarditis Cohort who may Safely Resume Sports Activities 3 Months after Diagnosis

International cardiovascular society recommendations to return to sports activities following acute myocarditis are based on expert consensus in the absence of prospective studies. We prospectively enrolled 30 patients with newly diagnosed myocarditis based on clinical parameters, laboratory measurements and cardiac magnetic resonance imaging with mildly reduced or pre served left ventricular ejection fraction (LVEF) with a follow-up of 12 months. Cessation of physical activity was recommended for 3 months. The average age was 35 (19–80) years with 73% male patients. One case of non-sustained ventricular tachycardia was recorded during 48-h-Holter electrocardiogram. Except for this case, all patients were allowed to resume physical exercise after 3 months. At 6- (n = 26) and 12-month (n = 19) follow-up neither cardiac events nor worsening LVEF were recorded. The risk of cardiac events at 1 year after diagnosis of myocarditis appears to be low after resumption of exercise after 3 months among patients who recover from acute myocarditis