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

This paper studies automorphisms and monomorphisms of direct products $\Gamma=\Gamma_1\times\cdots\times\Gamma_r$ of finitely generated virtually solvable minimax groups, a class containing all virtually polycyclic groups. Under an…

Let $p$ be an odd prime number, and $F$ a nonarchimedean local field of residual characteristic $p$. We classify the smooth, irreducible, admissible genuine mod-$p$ representations of the twofold metaplectic cover…

In this paper we study irreducible matrix representations of the welded braid group $WB_n$, also known as the group of conjugating automorphisms of a free group $F_n.$ We prove that $WB_n$ has no irreducible representations of dimension…

We present a family of index 1 abelian current graphs whose derived embeddings can be modified into triangulations of $K_{12s}$ for $s \geq 4$. Our construction is significantly simpler than previous methods for finding genus embeddings of…

We study the 1-dimensional Heisenberg antiferromagnet with s=1/2 using a Majorana representation of the s=1/2 spins. A simple Hartree-Fock approximation of the resulting model gives a bilinear fermionic description of the model. This…

We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…

We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. These representations proved to be useful for the construction of abelian varieties…

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

We discuss a new mechanism in which non-perturbative quantum gravity effects directly generate a Majorana mass for the neutron. In particular, in string theory, exotic instantons can generate an effective six quark operator by calculable…

Axial algebras are a class of non-associative commutative algebras whose properties are defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturally associated group of automorphisms and thus axial algebras…

As part of the programme to re-compute the character tables of all the groups in the Atlas we re-compute the character table of $\mathbb M$, the Monster simple group. We operate under the uniqueness hypotheses of $\mathbb M$ and the…

For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $\mathcal{H}_K$,…

The Donald-Flanigan conjecture asserts that any group algebra of a finite group has a separable deformation. We apply an inductive method to deform group algebras from deformations of normal subgroup algebras, establishing an infinite…

Suppose that $G$ is the group of $F$-points of a connected reductive group over $F$, where $F/\mathbb{Q}_p$ is a finite extension. We study the (topological) irreducibility of principal series of $G$ on $p$-adic Banach spaces. For unitary…

We prove that for any prime $\ell$, any finite group has as many irreducible complex characters of degree prime to $\ell$ as the normalizers of its Sylow $\ell$-subgroups. This equality was conjectured by John McKay. The conjecture was…

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by…

Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess algebra which has the Monster sporadic simple group as its…

Let $N$ be normal subgroup of a finite group $G$, $p$ be a prime, $P$ be a Sylow $p$-subgroup of $G$ and $\theta$ be a $P$-invariant irreducible character of $N$. Suppose that $G/N$ is a $p$-solvable group. In this note we show that,…