Canonical bases arising from quantum symmetric pairs

We develop a general theory of canonical bases for quantum symmetric pairs (\mathbf{U}, \mathbf{U}^\imath) with parameters of arbitrary finite type. We construct new canonical bases for the simple integrable $\mathbf{U}$-modules and their tensor products regarded as \mathbf{U}^\imath-modules. We also construct a canonical basis for the modified form of the $\imath$quantum group \mathbf{U}^\imath. To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank one), and integrality of the intertwiners.Comment: v1, 76 pages. v2, 62 pages, much shortened appendix, modified introduction and other corrections, to appear in Invent. Mat

Precursor problem and holographic mutual information

The recent proposal of Almheiri et al.http://arxiv.org/abs/1411.7041, together with the Ryu-Takayanagi formula, implies the entanglement wedge hypothesis for certain choices of boundary subregions. This fact is derived in the pure AdS space. A similar conclusion holds in the presence of quantum corrections, but in a more restricted domain of applicability. We also comment on http://arxiv.org/abs/1601.05416 and some similarities and differences with this workComment: 13 pages, 1 figur

Force/torque and tactile sensors for sensor-based manipulator control

The autonomy of manipulators, in space and in industrial environments, can be dramatically enhanced by the use of force/torque and tactile sensors. The development and future use of a six-component force/torque sensor for the Hermes Robot Arm (HERA) Basic End-Effector (BEE) is discussed. Then a multifunctional gripper system based on tactile sensors is described. The basic transducing element of the sensor is a sheet of pressure-sensitive polymer. Tactile image processing algorithms for slip detection, object position estimation, and object recognition are described

Deduction of the quantum numbers of low-lying states of 6-nucleon systems based on symmetry

The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be mainly {4,2} and {2,2,2}.Comment: 8 pages, no figure