Related papers: Symmetry Groups of $A_n$ Hypergeometric Series

This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…

We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…

Motivated by problems arising in the complex analysis of perturbative quantum field theory, we investigate the homology of finite unions of certain non-degenerate quadratic affine hypersurfaces of complex dimension $n$ in general position.…

We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

In this paper we explore the structure of certain generalized isometries of the special orthogonal group $SO(n)$ which are transformations that leave any member of a large class of generalized distance measures invariant. This gives us a…

We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries…

We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that…

We find all irreducible hypergeometric sheaves whose geometric monodromy group is finite, almost quasisimple and has the projective special linear group $PSL_n(q)$ with $n\geq 3$ as a composition factor. We use the classification of…

We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N>=1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six…

We prove a conjecture of Cohn and Propp, which refines a conjecture of Bosley and Fidkowski about the symmetry of the set of alternating sign matrices (ASMs). We examine data arising from the representation of an ASM as a collection of…

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups $\mathrm{Sym}(n)$ (in the sofic case) or the finite…

Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3--manifold groups. We investigate strongly…

The symmetric group S_n acts on the skew polynomial ring A=k_{-1}[x_1,..., x_n] as permutations. For subgroups G of S_n we consider properties of the ring of invariants A^G. We show that A^G is always Artin-Schelter Gorenstein, and we…

We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…

This paper aims to establish the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties.…

In this paper, we show that affine extensions of non-crystallographic Coxeter groups can be derived via Coxeter-Dynkin diagram foldings and projections of affine extended versions of the root systems E_8, D_6 and A_4. We show that the…

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain $N=2$ supergravity theories, where dimensional reduction induces a mapping between {\em special} real, K\"ahler…

These notes expand upon our lectures on {\em profinite rigidity} at the international colloquium on randomness, geometry and dynamics, organised by TIFR Mumbai at IISER Pune in January 2024. We are interested in the extent to which groups…