The Galactic cosmic-ray Sun shadow observed by HAWC

The magnetic field of the Solar corona is difficult to measure directly. However, indirect observations of the solar corona are possible using the deficit in flux of cosmic rays coming from the direction of the Sun. Low-energy cosmic rays (~GeV) are deflected by the inner magnetic field of the Sun and the interplanetary magnetic field frozen into the solar wind. In contrast, high-energy cosmic rays (~TeV and above) are absorbed in the Sun's photosphere producing a shadow in the Sun's nominal position viewed from Earth. Several ground-based instruments have observed the effects of the heliospheric magnetic field on the size of the sun shadow and its position. The High-Altitude Water Cherenkov Observatory (HAWC) is an air shower array located in the central region of Mexico that observes TeV cosmic rays at a rate of about 15 kHz. in this work, we present preliminary images of the sun shadow from data collected by HAWC during 2013 and 2014 for different energy ranges.Comment: Presented at the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. See arXiv:1508.03327 for all HAWC contribution

Quantization of canonical cones of algebraic curves

We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve C, based on the theory of formal pseudodifferential operators. When C is a complex curve with Poincar\'e uniformization, we propose another, equivalent construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a presentation of the quantum algebra when C is a rational curve, and discuss the problem of constructing algebraically "differential liftings"

Weight function for the quantum affine algebra Uq(A2(2))U_q(A_2^{(2)})

In this article, we give an explicit formula for the universal weight function of the quantum twisted affine algebra $U_q(A_2^{(2)})$. The calculations use the technique of projecting products of Drinfeld currents onto the intersection of Borel subalgebras of different types.Comment: 25 page

SOS model partition function and the elliptic weight functions

We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum affine algebra $U_{q}(\hat{\mathfrak{sl}}_{2})$ in its current realization. A generalization is proved for the the elliptic current algebra [arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of total currents are calculated explicitly and are represented as integral transforms of the product of the total currents. We prove that the kernel of this transform is proportional to the partition function of the SOS model with domain-wall boundary conditions.Comment: 21 pages, 5 figures, requires iopart packag