Related papers: On vector-valued twisted conjugate invariant funct…
We study the shifted convolution sum of the divisor function and some other arithmetic functions.
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
We give a concrete description of the category of G-equivariant vector bundles on certain affine G-varieties (where G is a reductive linear algebraic group over an algebraically closed field of characteristic 0) in terms of linear algebra…
We prove sharp weighted estimates for $r$-variations of averages and truncated singular integrals on suitable spaces of homogeneous type, including homogeneous nilpotent Lie groups.
The representations of dimension vector $\alpha$ of the quiver Q can be parametrised by a vector space $R(Q,\alpha)$ on which an algebraic group $\Gl(\alpha)$ acts so that the set of orbits is bijective with the set of isomorphism classes…
To any Hamiltonian action of a reductive algebraic group $G$ on a smooth irreducible symplectic variety $X$ we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles our…
It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge symmetries close for arbitrary gauge group.…
The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are discussed.
This thesis deals with the conjugacy problem in groups and its twisted variants. We analyze recent results by Bogopolski, Martino, Maslakova and Ventura on the twisted conjugacy problem in free groups and its implication for the conjugacy…
We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric…
We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…
It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.
Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invariant theory for reductive groups and how it is used to…
This paper constructs a representation of a Hecke algebra on a vector space spanned by the involutions in a Coxeter group.
We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this…
I adapt a recently introduced method for integrating over the unitary group (S. Aubert and C.S. Lam, J.Math.Phys. 44, 6112-6131 (2003)) to the orthogonal group. I derive explicit formulas for a number of one, two and three-vector integrals,…
This paper shows how a family of function spaces (coined as Assiamoua spaces) plays a fundamental role in the Fourier analysis of vector-valued functions compact groups. These spaces make it possible to transcribe the classic results of…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
The conjugate problem in stochastic optimal control can be formulated in terms of operators conjugated to the operators of stochastic integration [1, 2, 3]. In this paper we study some of such operators acting on the spaces of progressively…
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…