Related papers: Spin networks and SL(2,C)-Character varieties

A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is…

We propose a cyclic coefficient $R$ which represents the cyclic characteristics of complex networks. If the network forms a perfect tree-like structure then $R$ becomes zero. The larger value of $R$ represents that the network is more…

In this paper we further describe the features of the topological space $K(R)$ obtained from the loop nerve of $R$, for $R=(S,T)$ a bi-secondary structure. We will first identify certain distinct combinatorial structures in the arc diagram…

We compute the fundamental class (in the extended Bloch group) for representations of fundamental groups of 3-manifolds to SL(4,R) that factor over SL(2,C), in particular for those factoring over the isomorphism PSL(2,C) = S0(3,1). We also…

For a finite group, it is interesting to determine when two ordinary irreducible representations have the same $p$-modular reduction; that is, when two rows of the decomposition matrix in characteristic $p$ are equal, or equivalently when…

We describe the (P)SL(2,C) character varieties of all 2-bridge knots and the diagonal character varieties for all 2-bridge links in terms of a set of polynomials defined using Farey recursion.

An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function f:S->S that satisfies f(xy)=f(y)f(x) and f(f(x))=x for all x,y in S. The set I(S) of all such involutions on S generates a…

We classify the connected Lie subgroups of the symplectic group $Sp(2,\mathbb{R})$ whose elements are matrices in block lower triangular form. The classification is up to conjugation within $Sp(2,\mathbb{R})$. Their study is motivated by…

We discuss `hd-compactifications' of $\SL(2,\bbK)$ for $\bbK=\bbC$ or $\bbR.$ These are compact manifolds with boundary on which both the Schwartz and the Harish-Chandra Schwartz spaces are shown to be relatively standard spaces of conormal…

The problem of source algebra equivalences between blocks at the ends of the maximal strings of spin blocks of the symmetric and alternating groups has recently been settled, but so far there has not even been a candidate of the tilting…

For n at least 3, let SAut(F_n) denote the unique subgroup of index two in the automorphism group of a free group. The standard linear action of SL(n,Z) on R^n induces non-trivial actions of SAut(F_n) on R^n and on S^{n-1}. We prove that…

We give necessary and sufficient conditions for the existence of pin+, pin- and spin structures on Riemannian manifolds with holonomy group $Z_2^k$. For any n>3 (resp. n>5) we give examples of pairs of compact manifolds (resp. compact…

We study the relationship between Ng's abelian cord ring and SL(2,C) characters of the two-fold branched cover $\Sigma(K)$. Augmentations, and their corresponding rank, play a central role in the relationship. Our study also leads to a…

We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this…

We apply Godsil-McKay switching to the symplectic graphs over $\mathbb{F}_2$ with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new…

We investigate how SL(2,Z) duality is realized in nonrelativistic type IIB superstring theory, which is a self-contained corner of relativistic string theory. Within this corner, we realize manifestly SL(2,Z)-invariant (p,q)-string actions.…

We show that the algebraic automorphism group of the SL(2,C) character variety of a closed orientable surface with negative Euler characteristic is a finite extension of its mapping class group. Along the way, we provide a simple…

We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL\_2 groups over imaginary quadratic integers on their associated symmetric space. On the way, we extend the torsion…

The cyclic graph of a group $G$ is the graph whose vertices are the nonidentity elements of $G$ and whose edges connect distinct elements $x$ and $y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain information about…

The ring of dual numbers over a ring $R$ is $R[\alpha] = R[x]/(x^2)$, where $\alpha$ denotes $x+(x^2)$. For any finite commutative ring $R$, we characterize null polynomials and permutation polynomials on $R[\alpha]$ in terms of the…