Let G be a connected reductive group over an algebraically closed field k of characteristic not 2; let θ ∈ Aut(G) be an involution and K = Gθ ⊆ G the fixed point group of θ and let P ⊆ G be a parabolic subgroup. The set K\G/P of (K , P)-double cosets in G plays an important role in the study of Harish Chandra modules. In [BH00] we gave a description of the orbits of symmetric subgroups in a fla...

Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra sl(n, C) is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-gro...

We propose and study two new computational models for quantum computation, and infer new insights about the circumstances that give quantum computers an advantage over classical ones. The bomb query complexity model is a variation on the query complexity model, inspired by the Elitzur-Vaidman bomb tester. In this model after each query to the black box the result is measured, and the algorithm ...

In this paper we study the homogeneous conic system F : Ax = 0, x ∈ C \ {0}. We choose a point s̄ ∈ intC∗ that serves as a normalizer and consider computational properties of the normalized system Fs̄ : Ax = 0, s̄T x = 1, x ∈ C. We show that the computational complexity of solving F via an interior-point method depends only on the complexity value θ of the barrier for C and on the symmetry of the ...

where E`n denotes the group of `-torsion points of E. The Galois group GK = Gal(K̄/K) acts continuously on T` and therefore on V`. In a series of works ([5], [6], [8], [9]), Serre investigated the image, Γ`, of GK in GL(V`). If E has complex multiplication over C, Γ` is contained in a Cartan subgroup of GL(V`) (resp. the normalizer of a Cartan) if K contains (resp. does not contain) the endomorp...

A q-analog of a Steiner system (briefly, q-Steiner system), denoted by S = Sq[t, k, n], is a set of k-dimensional subspaces of F n q such that each t-dimensional subspace of Fq is contained in exactly one element of S. Presently, q-Steiner systems are known only for t = 1 and in the trivial cases t = k and k = n. In this paper, the first known nontrivial q-Steiner systems with t ≥ 2 are constru...

Methods for determining a generating set for the normalizer of a finite group of n X n integral matrices, i.e., an «-dimensional crystallographic point group, are discussed. Necessary and sufficient conditions for the finiteness of such a normalizer are derived, and several examples of the application of the methods to cases when the normalizer is infinite are presented. This is the third in a ...

For a group G, let U be the group of units of the integral group ring ZG. The group G is said to have the normalizer property if NU (G) = Z(U)G. It is shown that Blackburn groups have the normalizer property. These are the groups which have non-normal finite subgroups, with the intersection of all of them being nontrivial. Groups G for which class-preserving automorphisms are inner automorphism...

The general problem of computing the normalizer, in a finite permutat ion group G, of a subgroup H has long been recognized as being unusually difficult to solve efficiently. The corresponding problem for centralizers is much easier, although this too has some bad cases. The solution to the centralizer problem is relatively simple and probably difficult to improve upon, whereas there seems to b...