Related papers: ${\rm SL}(3,\mathbb{C})$-character varieties of tw…

We study the local structure of the representation variety of a knot group into SL(n,C) at certain diagonal representations. In particular we determine the tangent cone of the representation variety at these diagonal representations, and…

We propose a generalization of Carmichael numbers, where the multiplicative group $\mathbb G_\mathrm{m} = \mathrm{GL}(1)$ is replaced by $\mathrm{GL}(m)$ for $m\geq 2$. We prove basic properties of these families of numbers and give some…

We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.

An SL_n-character of a group G is the trace of an SL_n-representation of G. We show that all algebraic relations between SL_n-characters of G can be visualized as relations between graphs (resembling Feynman diagrams) in any topological…

We obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$.…

In this paper we address the problem of constructing a class of representations of Clifford algebras that can be named "alphabetic (re)presentations". The Clifford algebras generators are expressed as m-letter words written with a…

We present an algorithm for the explicit numerical calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients, based on the Gelfand-Tsetlin pattern calculus. Our algorithm is well-suited for numerical implementation; we include a computer…

Three fully variational formulations of the complete-active space coupled-cluster (CASCC) method are derived. The formulations include the ability to approximate the model vectors by smooth manifolds, thereby opening up the possibility for…

We define an $SL_2(\mathbb{R})$-Casson invariant of closed 3-manifolds. We also observe procedures of computing the invariants in terms of Reidemeister torsions. We discuss some approach of giving the Casson invariant some gradings.

In this paper we compute the character values of highest weight representations for classical groups of types A_n, B_n, C_n, D_n and the Exceptional group G_2 at all conjugacy classes of order 2. We prove that these character values, if…

We describe the relation between G-character varieties, $X_G(\Gamma)$, and $G/H$-character varieties, where $H$ is a finite, central subgroup of $G.$ In particular, we find finite generating sets of coordinate rings $C[X_{G/H}(\Gamma)]$ for…

Congruential pseudorandom number generators rely on good multipliers, that is, integers that have good performance with respect to the spectral test. We provide lists of multipliers with a good lattice structure up to dimension eight and up…

We explicitly compute the McKay quivers of small finite subgroups of $GL(2,\mathbb{C})$ relative to the natural representation, using character theory and the McKay quivers of finite subgroups of $SU(2)$. We present examples that shows the…

For a field F with discrete valuation and residue field $k$ we relate the third homology of SL_2(F) with half-integral coefficients to the third homology of SL_2(k) and a certain refined scissors congruence group of k. As an application, we…

We obtain the formula computing the number of isomorphic classes of element systems with characters over finite commutative group $G$.

We calculate a genus-one FJRW invariant of an LG pair $(W_3=x_1^3+x_2^3+x_3^3, \mu_3)$ via two different methods. In the first method, we apply the cosection localization technique to get a genus-one three-spin virtual class explicitly and…

This paper presents an analysis of primitive permutation groups of degree $3p$, where $p$ is a prime number, analogous to H. Wielandt's treatment of groups of degree $2p$. It is also intended as an example of the systematic use of…

Let p > 2 be a prime number and let N be any rational integer. We consider the p-class groups Cl(L), Cl(M) of the fields $L:=Q(N^{1/p})$ and $M:=Q(N^{1/p},\mu_p)$, by comparison with the p-torsion groups T(L) and T(M) of the abelian…

By means of parametrized presentations of finite metabelian 3-groups, it is proved that the coclass cc(M) of the second 3-class group M=Gal(F_3^2(K)/K) of any algebraic number field K with elementary bicyclic 3-class group Cl_3(K)=(3,3) is…

We use the properties of the refined Bloch group of a field to prove that H_3 of SL_2 of a global field is never finitely generated, and to calculate - up to some 2-torsion - H_3 of SL_2 of local fields with finite residue field of odd…