Related papers: Modular Reduction in Abstract Polytopes

In this article, we study the combinatorics of congruence subgroups of the modular group. More precisely, we consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of…

Using combinatorics of Young tableaux, we give an explicit construction of irreducible graded modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\lambda}$ of type $A_{n}$. Our construction is compatible…

By a new orthogonal direct sum decomposition $E_{M} = Y \oplus Z$, which $Z$ is related to $\Delta u_i(i=1,2,3,....,M)$, and a new functional $I(u)$, the method in [2] is improved to obtain new multiple periodic solutions with negativity…

We give a good reduction criterion for proper polycurves with sections,i.e., successive extensions of family of curves with section, under mild assumption. This criterion is a higher dimensional version of the good reduction criterion for…

This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are…

We continue our investigations of bilinear sums with modular square roots and the large sieve for square moduli in our recent article "On bilinear sums with modular square roots and applications II", arXiv:2603.00768. In the present…

We compute and analyse the moduli space of those real projective structures on a hyperbolic 3-orbifold that are modelled on a single ideal tetrahedron in projective space. Parameterisations are given in terms of classical invariants,…

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…

In this work, we describe the moduli of triples of points in quaternionic projective space which define uniquely the congruence classes of such triples relative to the action of the isometry group of quaternionic hyperbolic space ${\rm…

Following Nazarov's suggestion~\cite{Naz1}, we refer to the cyclotomic Nazarov-Wenzl algebra as the cyclotomic Brauer algebra. When the cyclotomic Brauer algebra is isomorphic to the endomorphism algebra of $M_{I_i, r}$-- the tensor product…

This survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura varieties with parahoric level structure…

Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequently used and studied. These forms are upper-triangular…

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case…

We present a theory of reduction of binary quadratic forms with coefficients in Z[lambda], where lambda is the minimal translation in a Hecke group. We generalize from the modular group Gamma(1) = SL(2,Z) to the Hecke groups and make…

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are…

This work proposes a novel, general and robust method of determining bond micromoduli for anisotropic linear elastic bond-based peridynamics. The problem of finding a discrete distribution of bond micromoduli that reproduces an anisotropic…

We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type $G(r,p,n)$ over field of any (coprime to $p$) characteristic. We give explicit formulas for the number of simple modules over these cyclotomic Hecke…