Like the LR-tableau, a socle tableau is given as skew diagram with certain entries. Unlike in entries are weakly increasing each row, strictly column and satisfy modified lattice permutation property. In study of embeddings subgroup finite abelian p $p$ -group, tableaux occur isomorphism invariants, they by series subgroup. We show that can be realized some embedding. Moreover, an embedding LR-...

Using a variant of an unpublished argument due to Agol, we show that irreducible right-angled Coxeter group on n ? 3 ${n \geqslant 3}$ vertices embeds as thin subgroup uniform arithmetic lattice in indefinite orthogonal O ( p , q ) $\mathrm{O}(p, q)$ for some 1 $p, 1$ satisfying + = $p+q=n$ .

We use the automorphism group Aut(H), of holes in the lattice L8 = A2 ⊕ A2 ⊕ D4, as the starting point in the construction of sphere packings in 10 and 12 dimensions. A second lattice, L4 = A2 ⊕ A2, enters the construction because a subgroup of Aut(L4) is isomorphic to Aut(H). The lattices L8 and L4, when glued together through this relationship, provide an alternative construction of the lamin...

We show that the number of rational points a subgroup inside toric variety over finite field defined by homogeneous lattice ideal can be computed via Smith normal form matrix whose columns constitute basis lattice. This generalizes and yields concise geometric proof same fact proven purely algebraically Lopez Villarreal for case projective space standard dimension one. also prove Nullstellensat...

Let G = PSL2(F) where F = R,C, and consider the space Z = (Γ1 × Γ2)\(G × G) where Γ1 < G is a co-compact lattice and Γ2 < G is a finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint [2] gives a classification of all ergodic invariant Radon measures on Z for the diagonal G-action. In this paper, for a horospherical subgroup N of G, we classify all ergodic, conservative, ...

We study the trace set of commutator subgroup Γ ( 2 ) , a type Local-Global problem about thin groups. determine local obstructions and then use correspondence between binary quadratic forms hyperbolic matrices to find some global obstructions. develop probabilistic argument for existence sufficiently large admissible traces by modeling elements as non-backtracking random walks in 2-dimensional...

Derivative lattices associated with partially ordered linear spaces over skew fields are considered. Properties of the convex projective geometry $$ \mathcal{L} for a space FV field F investigated. The convexity subspaces means Abelian (ab-convexity), which is based on definition subgroup group. It shown that ab-convex directed plays theory same role as subgroups groups. We obtain element-wise ...

Abstract There are many families of functions on partitions, such as the shifted symmetric functions, for which corresponding q -brackets quasimodular forms. We extend these so that a congruence subgroup. Moreover, we find subspaces -bracket is modular form. These results follow from properties Taylor coefficients strictly meromorphic quasi-Jacobi forms around rational lattice points.

We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory of Ehrhart polynomials to obtain properties of modular and integral flow polynomials. The emphasis is on the geometrical treatment through subgroup arrangeme...