Related papers: The orbit method for unipotent groups over finite …

We establish a fine expansion for the geometric part of the Arthur-Selberg trace formula (as it was conjectured by Werner Hoffmann). For the general linear group, we deduce an expression for the contributions of regular by blocks unipotent…

We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters…

Using method of inducing, irreducible unitary representation of Cayley--Klein orthogonal groups were constructed. There was proved that Kirilov's method of orbits is relevant for study of the behavior of irreducible representations under…

The purpose of this paper is to propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field (genus>1) over a given ground field of characteristic >2 as well as over its algebraic extensions.

We show that a finite unitary group which has orbits spanning the whole space is necessarily the setwise stabilizer of a certain orbit.

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In…

The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…

We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

In this paper, we construct certain unipotent representations for the real orthogonal group and the metaplectic group in the sense of Vogan. Our construction is based on quantum induction which involves the compositions of even number of…

We determine the fundamental group of period domains over finite fields.

In this paper we start a classification of certain global integrals. First, we use the language of unipotent orbits to write down a family of global integrals. We then classify all those integrals which satisfy the dimension equation we…

Let U be a unipotent group over the field of complex numbers C, acting on a complex algebraic variety X. Assume that there exists a surjective morphism of complex algebraic varieties f: X --> Y whose fibres are orbits of U. We show that if…

Computations in the cohomology of finite groups.

We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator…

We give an algorithm which computes a presentation for a subgroup, denoted $\AM_{g,1,p}$, of the automorphism group of a free group. It is known that $\AM_{g,1,p}$ is isomorphic to the mapping-class group of an orientable genus-$g$ surface…

We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.

We compute the equivariant Bauer-Furuta degree, when a finite group acts freely on a spin 4-manifold. In the case when the group is cyclic of order power of two, Bryan gave a formula and its applications. We have treated the case when the…

In this paper we describe various applications of the Riemann-Hilbert method to the theory of orthogonal polynomials on the line and on the circle.

For simple algebraic groups defined over algebraically closed fields of good characteristic, we give upper bounds on the covering numbers of unipotent conjugacy classes in terms of their (co)ranks and in terms of their dimensions.