Weights 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.

Multiple Orthogonal Polynomials for Classical Weights

A new set of special functions is described which has a wide range of applications, from number theory to integrability of non-linear dynamical systems. We study multiple orthogonal polynomials with respect to p > 1 weights satisfying Pearson’s equation. In particular, we give a classification of multiple orthogonal polynomials with respect to classical weights which is based on properties of t...

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...