Conductors and newforms for U(1,1)
Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms forU (1, 1)(F), building on previous work onSL2(F). This theory is analogous to the results of Casselman forGL2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGLn(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit formulae for newforms.
On local newforms for unramified U(2, 1)
Let G be the unramified unitary group in three variables defined over a p-adic field F with p ≠ 2. In this paper, we investigate local newforms for irreducible admissible representations of G. We introduce a family of open compact subgroups {Kn}n≥0 of G to define the local newforms for representations of G as the Kn-fixed vectors. We prove the existence of local newforms for generic representations and the multiplicity one property of the local newforms for admissible representations.
L-band 3D imaging of an Alpine Glacier: Results from the AlpTomoSAR campaign
In this paper we present results from the tomographic analysis of L-Band SAR data acquired in February/March 2014 over the Mittelbergferner glacier, Austrian Alps, during the ESA campaign AlpTomoSAR. The campaign includes coincident in-situ measurements of snow and ice properties, as well as high-frequency Ground Penetrating Radar (GPR) data acquired over a total length of 18 km. The analyses of three-dimensional TomoSAR data cubes shows the complexity of the glacier sub-surface scattering. Most areas are characterized by surface scattering in proximity of the Lidar surface, plus a complex pattern of in-depth volumetric scattering beneath. Various subsurface features observed in GPR transects at 600 MHz and 200 MHz clearly showed up in TomoSAR sections as well. In particular: firn bodies, crevasses, and even the bedrock down to 50 m below the ice surface.