On the connectedness of Deligne-Lusztig varieties

We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We also obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.Comment: v2: Revised Section 3, added Section 4. 6 page

An explicit Z'-boson explanation of the B->K*mu+mu- anomaly

A global fit to the recent B->K*mu+mu- data shows indications for a large new-physics contribution to the Wilson coefficient of the semi-leptonic vector operator. In this article we consider a simple Z'-boson model of 3-3-1 type that can accommodate such an effect without violating any other constraint from quark-flavour physics. Implications for yet unobserved decay modes such as B->Xsnunubar and longstanding puzzles like B->piK are also discussed. The Z'-boson masses required to address the observed anomaly lie in the range of 7 TeV. Such heavy Z' bosons evade the existing bounds from precision data and direct searches, and will remain difficult to discover even at a high-luminosity LHC. The potential of an ILC as well as the next generation of low-energy parity-violation experiments in constraining the Z'-boson parameter space is also examined.Comment: 20 pages, 5 figures; v2: Eqs. (9.2), (9.4) and (9.5) corrected, typos fixed and references added; matches version published in JHE

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