We consider Krammer’s representation of the pure braid group on three strings: P3 → GL 3, Z t±1, q±1 , where t and q are indeterminates. As it was done in the case of the braid group, B3, we specialize the indeterminates t and q to nonzero complex numbers. Then we present our main theorem that gives us a necessary and sufficient condition that guarantees the irreducibility of the complex specia...

We give an explicit L–representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the ” pure” case such a representation was already used by M. Sato in holonomic field theory. We study both ”pure” and ” mixed” cases. In the compact case we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions we orient our find...

2 Lifting results 4 2.1 Pure inner forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Twisting the representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Rational orbits in the twisted representation . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 A cohomological obstruction to lifting invariants . . . . . . . . . . . . . . . ...

Abstract Consider a reductive linear algebraic group G acting linearly on polynomial ring S over an infinite field; key examples are the general group, symplectic orthogonal and special with classical representations as in Weyl’s book: For consider direct sum of copies standard representation dual; other cases, take representation. The invariant rings respective cases determinantal rings, defin...

We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using knowledge from the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the xand ydimensions. One model features a discrete representation on the x-axis (strip width) and a continuous representation ...

The antilinear operator representation of bipartite pure states of the relative state formulation of quantum mechanics is applied to describe quantum teleportation schemes utilizing an arbitrary pure state as the entangled resource. Bennett type teleportation schemes with nonmaximally entangled pure states are characterized and the notion of ‘entanglement matching’ is introduced in general. Exa...