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

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 #

Formation of Sco X-1 induced by anomalous magnetic braking of Ap/Bp stars

Sco X-1 is the brightest persistent X-ray in the sky. It is generally believed that Sco X-1 is a low-mass X-ray binary containing a neutron star accreting from a low-mass donor star where mass transfer is driven by the magnetic braking. However, the mass transfer rate predicted by the standard magnetic braking model is at least one order of magnitude lower than the one inferred by X-ray luminosity. In this work, we investigate whether this source could evolved from an intermediate-mass X-ray binary including Ap/Bp stars with a slightly strong magnetic field of 300 - 1000 G. The coupling between the magnetic field and an irradiation-driven wind induced by the X-ray flux from the accretor can yield a strong magnetic braking, which could give rise to a relatively high mass transfer rate. According to the observed orbital period, the mass transfer rate, the mass ratio, and the donor star spectral type, the progenitor of Sco X-1 should be an intermediate-mass X-ray binary including a 1.6 $-$ 1.8 $\rm M_{\odot}$ Ap/Bp donor star in a 1.3 $-$ 1.5 day orbit. Therefore, we propose that anomalous magnetic braking of Ap/Bp stars provides an alternative evolutionary channel to a part of luminous X-ray sources.Comment: 7 pages, 5 figures, accepted for publication in A&

Fast orbital shrinkage of black hole X-ray binaries driven by circumbinary disks

Recently, the black hole X-ray binary (BHXB) Nova Muscae 1991 has been reported to be experiencing an extremely rapid orbital decay. So far, three BHXBs have anomalously high orbital period derivatives, which can not be interpreted by the standard stellar evolution theory. In this work, we investigate whether the resonant interaction between the binary and a surrounding circumbinary (CB) disk could produce the observed orbital period derivatives. Analytical calculations indicate that the observed orbital period derivatives of XTE J1118+480 and A0620-00 can originate from the tidal torque between the binary and a CB disk with a mass of $10^{-9}~\rm M_{\odot}$, which is approximately in agreement with the dust disk mass detected in these two sources. However, Nova Muscae 1991 was probably surrounded by a heavy CB disk with a mass of $10^{-7}~\rm M_{\odot}$. Based on the CB disk model and the anomalous magnetic braking theory, we simulate the evolution of the three BHXBs with intermediate-mass donor stars by using the MESA code. Our simulated results are approximately consistent with the observed donor star masses, orbital periods, and orbital-period derivatives. However, the calculated effective temperatures of the donor stars are higher than indicated by the observed spectral types of two sources.Comment: 6 pages, 5 figures, accepted for publication by ApJ

Evolution of black-hole intermediate-mass X-ray binaries: the influence of a circumbinary disc

Justham, Rappaport & Podsiadlowski (2006) recently suggested that black-hole low-mass X-ray binaries (BHLMXBs) with short orbital periods may have evolved from black-hole intermediate-mass X-ray binaries (BHIMXBs). In their model the secondaries in BHIMXBs are assumed to possess anomalously high magnetic fields, so that magnetic braking can lead to substantial loss of angular momentum. In this paper we propose an alternative mechanism for orbital angular momentum loss in BHIMXBs. We assume that a small fraction $\delta$ of the transferred mass from the donor star form a circumbinary disc surrounding the binary system. The tidal torques exerted by the disc can effectively drain orbital angular momentum from the binary. We have numerically calculated the evolutionary sequences of BHIMXBs, to examine the influence of the circumbinary disc on the binary evolution. Our results indicate when \delta\la 0.01-0.1 (depending on the initial orbital periods), the circumbinary disc can cause secular orbital shrinking, leading to the formation of compact BHLMXBs, otherwise the orbits always expand during the evolution. This scenario also suggests the possible existence of luminous, persistent BHLMXBs, but it suffers the same problem as in Justham, Rappaport & Podsiadlowski (2006) that, the predicted effective temperatures of the donor stars are significantly higher than those of the observed donor stars in BHLMXBs.Comment: 7 pages, 5 figures, accepted for publication in MNRA