515 research outputs found
Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
In this note we strenghten a theorem by Esnault-Schechtman-Viehweg which
states that one can compute the cohomology of a complement of hyperplanes in a
complex affine space with coefficients in a local system using only logarithmic
global differential forms, provided certain "Aomoto non-resonance conditions"
for monodromies are fulfilled at some "edges" (intersections of hyperplanes).
We prove that it is enough to check these conditions on a smaller subset of
edges.
We show that for certain known one dimensional local systems over
configuration spaces of points in a projective line defined by a root system
and a finite set of affine weights (these local systems arise in the geometric
study of Knizhnik-Zamolodchikov differential equations), the Aomoto resonance
conditions at non-diagonal edges coincide with Kac-Kazhdan conditions of
reducibility of Verma modules over affine Lie algebras.Comment: 10 pages, latex. A small error and a title in the bibliography are
correcte
Independent individual addressing of multiple neutral atom qubits with a MEMS beam steering system
We demonstrate a scalable approach to addressing multiple atomic qubits for
use in quantum information processing. Individually trapped 87Rb atoms in a
linear array are selectively manipulated with a single laser guided by a MEMS
beam steering system. Single qubit oscillations are shown on multiple sites at
frequencies of ~3.5 MHz with negligible crosstalk to neighboring sites.
Switching times between the central atom and its closest neighbor were measured
to be 6-7 us while moving between the central atom and an atom two trap sites
away took 10-14 us.Comment: 9 pages, 3 figure
An Integrable Model of Quantum Gravity
We present a new quantization scheme for gravity coupled to an
principal chiral field and a dilaton; this model represents a slightly
simplified version of stationary axisymmetric quantum gravity. The analysis
makes use of the separation of variables found in our previous work [1] and is
based on a two-time hamiltonian approach. The quantum constraints are shown to
reduce to a pair of compatible first order equations, with the dilaton playing
the role of a ``clock field''. Exact solutions of the Wheeler-DeWitt equation
are constructed via the integral formula for solutions of the
Knizhnik-Zamolodchiokov equations.Comment: 12 page
Heisenberg realization for U_q(sln) on the flag manifold
We give the Heisenberg realization for the quantum algebra , which
is written by the -difference operator on the flag manifold. We construct it
from the action of on the -symmetric algebra by the
Borel-Weil like approach. Our realization is applicable to the construction of
the free field realization for the [AOS].Comment: 10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a
reference added
Recombinant human perlecan DV and its LG3 subdomain are neuroprotective and acutely functionally restorative in severe experimental ischemic stroke
Despite recent therapeutic advancements, ischemic stroke remains a major cause of death and disability. It has been previously demonstrated that ~ 85-kDa recombinant human perlecan domain V (rhPDV) binds to upregulated integrin receptors (α2β1 and α5β1) associated with neuroprotective and functional improvements in various animal models of acute ischemic stroke. Recombinant human perlecan laminin-like globular domain 3 (rhPD
Chamber basis of the Orlik-Solomon algebra and Aomoto complex
We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so
called chamber basis. We consider structure constants of the Orlik-Solomon
algebra with respect to the chamber basis and prove that these structure
constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page
Gaudin model and its associated Knizhnik-Zamolodchikov equation
The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin
19-vertex model is used to solve the theory of Gaudin models associated with
the twisted R-matrix. We find the spectra and eigenvectors of the
independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz
method to show how the off-shell Gaudin equation solves the associated
trigonometric system of Knizhnik-Zamolodchikov equations.Comment: 20 pages,no figure, typos corrected, LaTe
Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces
We show that the Hirzebruch-Milnor class of a projective hypersurface, which
gives the difference between the Hirzebruch class and the virtual one, can be
calculated by using the Steenbrink spectra of local defining functions of the
hypersurface if certain good conditions are satisfied, e.g. in the case of
projective hyperplane arrangements, where we can give a more explicit formula.
This is a natural continuation of our previous paper on the Hirzebruch-Milnor
classes of complete intersections.Comment: 15 pages, Introduction is modifie
- …