Towards a Goldberg–Shahidi pairing for classical groups

Maximal prehomogeneous subspaces on classical groups

Suppose $G$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is‎ ‎the Lie algebra of the unipotent radical $N.$ Under the adjoint‎ ‎action of its stabilizer in $M,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.

Exponentiating in Pairing Groups

We study exponentiations in pairing groups for the most common security levels and show that, although the Weierstrass model is preferable for pairing computation, it can be worthwhile to map to alternative curve representations for the non-pairing group operations in protocols.

Classical Isomorphisms for Quantum Groups

The expressions for the R̂–matrices for the quantum groups SOq2(5) and SOq(6) in terms of the R̂–matrices for Spq(2) and SLq(4) are found, and the local isomorphisms of the corresponding quantum groups are established. On leave of absence from P.N.Lebedev Physical Institute, Theoretical Department, 117924 Moscow, Leninsky prospect 53, CIS.

Classical Groups

Constructive homomorphisms for classical groups

Let Ω ≤ GLd(q) be a quasisimple classical group in its natural representation and let ∆ = NGLd(q)(Ω). We construct the projection from ∆ to ∆/Ω and provide fast, polynomialtime algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent ∆/Ω as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of...