1. Geometry of primitive ideals. 1.1. Let G be a complex algebraic group with Lie algebra g. I would like to have a geometric picture for the structure of primitive ideals of the enveloping algebra U(g). The only universal answer known so far is the "orbit method," saying that primitive ideals should correspond to coadjoint orbits in the dual g* of g. Sometimes this principle doesn't work, howe...

Leading towards the classification of primitive commutative association schemes as the ultimate goal, Bannai and some of his school have been trying to • identify the major sources of (primitive) commutative association schemes, • collect known group-case primitive commutative association schemes, and • compute their character tables over the last twenty years. The construction of their charact...

Let F be the function field of a curve over p-adic field. D/F central division algebra prime exponent $\ell$ which is different from p. Assume that contains primitive ${\ell}^2$-th root unity. Then group $SK_1(D):=SL_1(D)/[D^*, D^*]$ trivial.

A 2&(v, k, 1) design D=(P, L) is a system consisting of a finite set P of v points and a collection L of a k-subset of P, called lines, such that each 2-subset of P is contained in precisely one line. We shall always assume that 2<k<v. Let G Aut(D) be a group of automorphisms of a 2&(v, k, 1) design D. The group G is said to be line-transitive (line-primitive, respectively) on D if G is transit...

In this paper we use the O’Nan–Scott Theorem and Aschbacher’s theorem to classify the primitive permutation groups of degree less than 2500. MSC: 20B15, 20B10 1 Historical Background The classification of the primitive permutation groups of low degree is one of the oldest problems in group theory. The earliest significant progress was made by Jordan, who in 1871 counted the primitive permutatio...

This paper introduces Hidden Identity-based Signatures (Hidden-IBS), a type of digital signatures that provide mediated signer-anonymity on top of Shamir’s Identity-based signatures. The motivation of our new signature primitive is to resolve an important issue with the kind of anonymity offered by “group signatures” where it is required that either the group membership list is public or that t...