Abstract. This article records basic topological, as well as homological properties of the space of homomorphisms Hom(π,G) where π is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If π is a free abelian group of rank equal to n, then Hom(π,G) is the space of ordered n–tuples of commuting elements in G. If G = SU(2), a complete calculation of the cohomology of ...

in this paper, the use of weighted pairwise likelihood instead of the full likelihood in estimating the parameters of the multivariate ar(1) is investigated. a closed formula for typical elements of the godambe information(sandwich information) is presented. some efficiency calculations are also given to discuss the feasibility andcomputational advantages of the weighted pairwise likelihood app...

The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are important pairwise commuting sets elements the algebra: Cherednik operators Jucys–Murphy whose simultaneous eigenfunctions nonsymmetric Macdonald polynomials, basis vectors irreducible modules algebra, respectively. For certain parameter values, it is possible for special to be with equal...

In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group G so that its non-commuting graph is L-integral.

For given non-abelian group G, the non-commuting (NC)-graph $Gamma(G)$ is a graph with the vertex set $G$ $Z(G)$ and two distinct vertices $x, yin V(Gamma)$ are adjacent whenever $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

Let G be the classical group, and let Hom ( Z m , ) denote space of commuting -tuples in . First, we refine formula for Poincaré series due to Ramras Stafa by assigning (signed) integer partitions permutations. Using refined formula, determine top term series, apply it prove dependence topology on parity rational hyperbolicity ? 2 Next, give a minimal generating set cohomology low dimensions. W...