Related papers: Spectral Measures for $G_2$ II: finite subgroups

Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the rank two Lie group $G_2$, including the McKay graphs for the irreducible representations of…

Spectral measures for fundamental representations of the rank two Lie groups $SU(3)$, $Sp(2)$ and $G_2$ have been studied. Since these groups have rank two, these spectral measures can be defined as measures over their maximal torus…

Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the compact connected rank two Lie group $SO(5)$ and its double cover the compact connected,…

We complete the computation of spectral measures for SU(3) nimrep graphs arising in subfactor theory, namely the SU(3) ADE graphs associated with SU(3) modular invariants and the McKay graphs of finite subgroups of SU(3). For the SU(2)…

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G_2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of N=1…

Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated alge bras of quantum symmetries and discover or recover, as a…

Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.

In this paper we study spectra of Laplacians of infinite weighted graphs. Instead of the assumption of local finiteness we impose the condition of summability of the weight function. Such graphs correspond to reversible Markov chains with…

We give the classification of all possible G-graphs for any small binary dihedral subgroup G in GL(2,C) and use this classification to give the combinatorial description of the special representations of G in terms of its maximal cyclic…

In this paper, we investigate homogeneous Riemannian geometry on real flag manifolds of the split real form of $\mathfrak{g}_2$. We characterize the metrics that are invariant under the action of a maximal compact subgroup of $G_2.$ Our…

Given a finite group $G$ and its representation $\rho$, the corresponding McKay graph is a graph $\Gamma(G,\rho)$ whose vertices are the irreducible representations of $G$; the number of edges between two vertices $\pi,\tau$ of…

For a graph $G$ of order $n$, the spectral sum of $G$ is defined to be the sum $\lambda_1(G) + \lambda_2(G)$, where $\lambda_1(G)$ (resp. $\lambda_2(G)$) is the largest (resp. second largest) adjacency eigenvalue of $G$. Ebrahimi, Mohar,…

In this paper we investigate relations between Koopman, groupoid and quasi-regular representations of countable groups. We show that for an ergodic measure class preserving action of a countable group G on a standard Borel space the…

Let $G$ be a Lie-group and $\Ga\subset G$ a cocompact lattice. For a finite-dimensional, not necessarily unitary representation $\om$ of $\Ga$ we show that the $G$-representation on $L^2(\Ga\bs G,\om)$ admits a complete filtration with…

Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then the harmonic…

The subdivision graph $\mathcal{S}(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. Let $G_1$ and $G_2$ be two vertex disjoint graphs. The \emph{subdivision-vertex join} of $G_1$ and $G_2$, denoted…

For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups,…

Let $A(G)$ be the adjacency matrix of a graph $G$ with $\lambda_{1}(G)$, $\lambda_{2}(G)$, ..., $\lambda_{n}(G)$ being its eigenvalues in non-increasing order. Call the number $S_k(G):=\sum_{i=1}^{n}\lambda_{i}^k(G) (k=0,1,...,n-1)$ the…

We present an explicit measurement in the Fourier basis that solves an important case of the Hidden Subgroup Problem, including the case to which Graph Isomorphism reduces. This entangled measurement uses $k=\log_2 |G|$ registers, and each…