Related papers: Structure of Loop Space at Finite $N$

In this paper we study invariant rings arising in the study of finite dimensional algebraic structures. The rings we encounter are graded rings of the form $K[U]^{\Gamma}$ where $\Gamma$ is a product of general linear groups over a field…

Let G be a finite group of complex n by n unitary matrices generated by reflections acting on C^n. Let R be the ring of invariant polynomials, and \chi be a multiplicative character of G. Let \Omega^\chi be the R-module of \chi-invariant…

The moduli space $M$ of semi-stable rank 2 bundles with trivial determinant over a complex curve carries involutions naturally associated to 2-torsion points on the Jacobian of the curve. For every lift of a 2-torsion point to a 4-torsion…

We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…

We investigate how effectively finite metric spaces can be distinguished by distance-based invariants. As model spaces, we consider regular polygons, cycle graphs, and their generalization, circular metric spaces, and as invariants we…

We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…

The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…

We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant…

In many physical problems or applications one has to study functions that are invariant under the action of a symmetry group G and this is best done in the orbit space of G if one knows the equations and inequalities defining the orbit…

Combining elements of twistor-space, phase space and Clifford algebras, we propose a framework for the construction and quantization of certain (quadric) varieties described by Lorentz-covariant multivector coordiantes. The correspondent…

Let $X$ and $Y$ be finite complexes. When $Y$ is a nilpotent space, it has a rationalization $Y \to Y_{(0)}$ which is well-understood. Early on it was found that the induced map $[X,Y] \to [X,Y_{(0)}]$ on sets of mapping classes is…

Ends and end cohomology are powerful invariants for the study of noncompact spaces. We present a self-contained exposition of the topological theory of ends and prove novel extensions including the existence of an exhaustion of a proper…

Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…

We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are…

We study the coefficients of a natural basis for the space of weak harmonic Maass forms of weight $5/2$ on the full modular group. The non-holomorphic part of the first element of this infinite basis encodes the values of the partition…

Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful…

An extended class of N=2 locally supersymmetric invariants with higher-derivative couplings based on full superspace integrals, is constructed. These invariants may depend on unrestricted chiral supermultiplets, on vector supermultiplets…