Related papers: The E-normal structure of odd dimensional unitary …
We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new $\Delta$-operator action on semidensities as the proper framework for Batalin-Vilkovisky formalism. We establish relations between…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…
Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to…
The Lorentz transformation group $SO(m,n)$ is a group of Lorentz transformations of order $(m,n)$, that is, a group of special linear transformations in a pseudo-Euclidean space of signature $(m,n)$ that leave the pseudo-Euclidean inner…
We review the current status of the construction of unitary representations of U-duality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal supergravity theories and on the N=2…
We prove that the extended Poincare group in (1+1) dimensions is non-nilpotent solvable exponential, and therefore that it belongs to type I. We determine its first and second cohomology groups in order to work out a classification of the…
The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…
We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as…
A subgroup $H$ of a group $G$ is said to be {pronormal} in $G$ if $H$ and $H^g$ are conjugate in $\langle H, H^g \rangle$ for every $g \in G$. Some problems in finite group theory, combinatorics, and permutation group theory were solved in…
When n is odd, consider the finite general linear and unitary groups of rank n, extended by the inverse transpose automorphism. There are elements in the extended groups which square to a regular unipotent element, and we evaluate the…
In this article we define a set of matrices analogous to Vaserstein-type matrices which was introduced in the paper `Serre's problem on projective modules over polynomial rings and algebraic K-theory' by Suslin-Vaserstein in 1976. We prove…
In this paper we look at a special type of discrete subgroups of $PSL_{n+1}(\Bbb{C})$ called Schottky groups. We develop some basic properties of these groups and their limit set when $n > 1$, and we prove that Schottky groups only occur in…
Let X be a non-empty finite set, E be a finite dimensional euclidean vector space and G a finite subgroup of O(E), the orthognal group of E. Suppose GG={U_i | i in X} is a finite set of linear lines in E and an orbit of G on which its…
Let $R$ be a finite commutative ring with unity $1_R$ and $k \in R$. Properties of one-sided $k$-orthogonal $n \times n$ matrices over $R$ are presented. When $k$ is idempotent, these matrices form a semigroup structure. Consequently new…
A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
We classify the non-Abelian anomaly of the Euclidean conformal group $SO(2n+1,1)$ in $2n$ dimensions via Stora-Zumino descent from its Euler invariant polynomial in $2n+2$ dimensions. In this way, we place the conformal anomaly on the same…
We define a model of 2 coupled SU(2) doublets of scalar fields in $4$ spacetime dimensions which have a rich structure of renormalization group (RG) flows to 1-loop when the SU(2) is broken to U(1). The model is pseudo-hermitian, $H^\dagger…
A 2-cell embedding of a graph $G$ into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags - mutually incident vertex-edge-face triples. In this paper, we classify the…