The nilpotent variety of W(1;n)pW(1;n)_{p} is irreducible

In the late 1980s, Premet conjectured that the nilpotent variety of any finite dimensional restricted Lie algebra over an algebraically closed field of characteristic $p>0$ is irreducible. This conjecture remains open, but it is known to hold for a large class of simple restricted Lie algebras, e.g. for Lie algebras of connected reductive algebraic groups, and for Cartan series $W, S$ and $H$. In this paper, with the assumption that $p>3$, we confirm this conjecture for the minimal $p$-envelope $W(1;n)_p$ of the Zassenhaus algebra $W(1;n)$ for all $n\geq 2$.Comment: 18 pages, Lemma 3.1 in [v2] is deleted and a few mistakes are correcte

On the Proximity Factors of Lattice Reduction-Aided Decoding

Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this aim, the proximity factors are defined to measure the worst-case losses in distances relative to closest point search (in an infinite lattice). Upper bounds on the proximity factors are derived, which are functions of the dimension $n$ of the lattice alone. The study is then extended to the dual-basis reduction. It is found that the bounds for dual basis reduction may be smaller. Reasonably good bounds are derived in many cases. The constant bounds on proximity factors not only imply the same diversity order in fading channels, but also relate the error probabilities of (infinite) lattice decoding and lattice reduction-aided decoding.Comment: remove redundant figure

Semiclassical Boltzmann theory of spin Hall effects in giant Rashba systems

For the spin Hall effect arising from strong band-structure spin-orbit coupling, a semiclassical Boltzmann theory reasonably addressing the intriguing disorder effect called side-jump is still absent. In this paper we describe such a theory of which the key ingredient is the spin-current-counterpart of the semiclassical side-jump velocity (introduced in the context of the anomalous Hall effect). Applying this theory to spin Hall effects in a two-dimensional electron gas with giant Rashba spin-orbit coupling, we find largely enhanced spin Hall angle in the presence of magnetic impurities when only the lower Rashba band is partially occupied.Comment: 6 pages, 1 figure, some more discussions added in this version, accepted by Frontiers of Physic

Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications

In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V. Lafforgue on the space of cuspidal automorphic forms, to the space of automorphic forms with compact support. This gives the Langlands parametrization for some quotient spaces of the latter, which is compatible with the constant term morphism.Comment: published versio

Combinatorial data of a free arrangement and the Terao conjecture

We present a combinatorial structure of generators of $D(\mathcal{A}).$ This structure permits us to detect the relationship between the combinatorial determined property and the singularity of vector field. Consequently, by using only combinatorial data, we have a basis of the module in free case and that yields a proof for the Terao's conjecture. We also verify the example of Ziegler and give a sufficient condition on combinatorial determined property of generators

Optimizing the RVB state on a triangular lattice: Presence of the long-range order

We present a Schwinger-boson approach for the RVB state of the spin-1/2 Heisenberg antiferromagnet on a triangular lattice. It is shown that Gutzwiller projection of the mean-field state that includes both antiferromagnetic and ferromagnetic decouplings leads to optimizing the RVB pair amplitudes within a self-consistent approximation. The resulting state yields, by Monte Carlo simulations, energies and spin-spin correlations in excellent agreement with the exact diagonalization result on finite lattices (up to 36 sites). We conclude that the optimized RVB wavefunction possesses a long-range three-sublattice order.Comment: 11 pages, plain LATEX (no local report #