Related papers: $2A$-Majorana Representations of $A_{12}$

Let $\mathbb{M}$ be the Monster finite simple group. We give an interpretation of certain discrete symmetries of a family of heterotic string compactifications to $1 + 1$ dimensions in terms of discrete symmetries of the Monster Lie algebra…

A collection $B$ of patterns is called inversion monotone if $\mathrm{av}_n^k(B)$, the number of $B$-avoiding permutations of length $n$ with $k$ inversions, is weakly increasing in $n$ for any fixed $k$. In 2012, Claesson, Jel\'inek and…

It is known that the Lawrence-Krammer representation of the Artin group of type $A_{n-1}$ based on the two parameters $t$ and $q$ that was used by Krammer and independently by Bigelow to show the linearity of the braid group on $n$ strands…

By introducing Frobenius morphisms $F$ on algebras $A$ and their modules over the algebraic closure ${{\bar \BF}}_q$ of the finite field $\BF_q$ of $q$ elements, we establish a relation between the representation theory of $A$ over ${{\bar…

Topological superconductors in one spatial dimension exhibiting a single Majorana bound state at each end are distinguished from trivial gapped systems by a Z_2 topological invariant. Originally, this invariant was calculated by Kitaev in…

The work of Bernstein-Zelevinsky and Zelevinsky gives a good understanding of irreducible subquotients of a reducible principal series representation of $GL_n(F)$, $F$ a $p$-adic field (without specifying their multiplicities which is done…

We study the numbers of involutions and their relation to Frobenius-Schur indicators in the groups $\mathrm{SO}^{\pm}(n,q)$ and $\Omega^{\pm}(n,q)$. Our point of view for this study comes from two motivations. The first is the conjecture…

We give a new construction of the moonshine VOA V^{\natural} over the real number field. We proved that V^{\natural} has a positive definite invariant bilinear form and its full automorphism group is the Monster simple group. We also…

A new class of locally unital and locally finite dimensional algebras $A$ over an arbitrary algebraically closed field is discovered. Each of them admits an upper finite weakly triangular decomposition, a generalization of an upper finite…

This paper is the first part of a series of papers aimed at improving the classification by Formanek of the irreducible representations of Artin braid groups of small dimension. In this paper we classify all the irreducible complex…

We derive integral representations in terms of the Macdonald functions for the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a<0$ and $a\not= -1,-2,\ldots $, generalizing known…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

We explain a conjecture relating the monster simple group to an algebraic variety that was discovered in a non-monstrous context.

We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of…

We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non irreducible representation $U$. The group $G$ is an arbitrary semidirect product whose normal factor $A$ is abelian and whose homogeneous factor…

In 2003, Cohn and Umans proposed a group-theoretic approach to bounding the exponent of matrix multiplication. Previous work within this approach ruled out certain families of groups as a route to obtaining $\omega = 2$, while other…

The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented…

Let $\sigma_1$ and $\sigma_2$ be commuting involutions of a semisimple algebraic group $G$. This yields a $Z_2\times Z_2$-grading of $\g=\Lie(G)$, $\g=\bigoplus_{i,j=0,1}\g_{ij}$, and we study invariant-theoretic aspects of this…

We give some conditions on a family of abelian covers of ${\mathbb P}^1$ of genus $g$ curves, that ensure that the family yields a subvariety of ${\mathsf A}_g$ which is not totally geodesic, hence it is not Shimura. As a consequence, we…

In this article we give an self contained existence proof for J. Conway's sporadic simple group Co_1 [4] using the second author's algorithm [14] constructing finite simple groups from irreducible subgroups of GL_n(2). Here n = 11 and the…