12,463 research outputs found
Combinatorial realizations of crystals via torus actions on quiver varieties
Consider Kashiwara's crystal associated to a highest weight representation of
a symmetric Kac-Moody algebra. There is a geometric realization of this object
using Nakajima's quiver varieties, but in many particular cases it can also be
realized by elementary combinatorial methods. Here we propose a framework for
extracting combinatorial realizations from the geometric picture: We construct
certain torus actions on the quiver varieties and use Morse theory to index the
irreducible components by connected components of the subvariety of torus fixed
points. We then discuss the case of affine sl(n). There the fixed point
components are just points, and are naturally indexed by multi-partitions.
There is some choice in our construction, leading to a family of combinatorial
models for each highest weight crystal. Applying this construction to the
crystal of the fundamental representation recovers a family of combinatorial
realizations recently constructed by Fayers. This gives a more conceptual proof
of Fayers' result as well as a generalization to higher level. We also discuss
a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some
references; v3: many small correction
Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost
We show that the class of antenna layouts for telescope arrays allowing cheap
analysis hardware (with correlator cost scaling as N log N rather than N^2 with
the number of antennas N) is encouragingly large, including not only previously
discussed rectangular grids but also arbitrary hierarchies of such grids, with
arbitrary rotations and shears at each level. We show that all correlations for
such a 2D array with an n-level hierarchy can be efficiently computed via a
Fast Fourier Transform in not 2 but 2n dimensions. This can allow major
correlator cost reductions for science applications requiring exquisite
sensitivity at widely separated angular scales, for example 21cm tomography
(where short baselines are needed to probe the cosmological signal and long
baselines are needed for point source removal), helping enable future 21cm
experiments with thousands or millions of cheap dipole-like antennas. Such
hierarchical grids combine the angular resolution advantage of traditional
array layouts with the cost advantage of a rectangular Fast Fourier Transform
Telescope. We also describe an algorithm for how a subclass of hierarchical
arrays can efficiently use rotation synthesis to produce global sky maps with
minimal noise and a well-characterized synthesized beam.Comment: Replaced to match accepted PRD version. 10 pages, 9 fig
Status of FNAL SciBooNE experiment
SciBooNE is a new experiment at FNAL which will make precision
neutrino-nucleus cross section measurements in the one GeV region. These
measurements are essential for the future neutrino oscillation experiments. We
started data taking in the antineutrino mode on June 8, 2007, and collected
5.19 \times 10^{19} protons on target (POT) before the accelerator shutdown in
August. The first data from SciBooNE are reported in this article.Comment: 3 pages, 3 figures. Proceedings of the 10th International Conference
on Topics in Astroparticle and Underground Physics (TAUP) 2007, Sendai,
Japan, September 11-15, 200
The Refined Topological Vertex
We define a refined topological vertex which depends in addition on a
parameter, which physically corresponds to extending the self-dual graviphoton
field strength to a more general configuration. Using this refined topological
vertex we compute, using geometric engineering, a two-parameter (equivariant)
instanton expansion of gauge theories which reproduce the results of Nekrasov.
The refined vertex is also expected to be related to Khovanov knot invariants.Comment: 70 Pages, 23 Figure
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