Related papers: Maximal stable lattices in representations over di…

In 2010, G\'{a}bor Cz\'{e}dli and E. Tam\'{a}s Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet [A cover-preserving embedding of semimodular lattices into geometric lattices,…

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…

Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice.…

Given a $G$-space $X$ and a non-trivial $G$-invariant ideal $I$ of subsets of $X$, we prove that for every partition $X=A_1\cup\dots\cup A_n$ of $X$ into $n\ge 2$ pieces there is a piece $A_i$ of the partition and a finite set $F\subset G$…

In this fith part, (with the notations of the preceding parts) we make the following hypothesis: $(W,S)$ is a Coxeter system, irreducible, $2$-spherical and $S$ is of cardinality $3$. Let $R:W\to GL(M)$ be a reducible reflection…

We show that the closed convex hull of any one-dimensional semi-algebraic subset of R^n has a semidefinite representation, meaning that it can be written as a linear projection of the solution set of some linear matrix inequality. This is…

Let G be a connected simple linear Lie group and H in G a symmetric subgroup such that the corresponding symmetric space G/H is non-compactly causal. We show that any irreducible unitary representation of G leads naturally to a net of…

Let $GL_M$ be general linear Lie group over the complex field. The irreducible rational representations of the group $GL_M$ are labeled by pairs of partitions $\mu$ and $\tilde\mu$ such that the total number of non-zero parts of $\mu$ and…

We classify all triples $(G,V,H)$ such that $SL_n(q)\leq G\leq GL_n(q)$, $V$ is a representation of $G$ of dimension greater than one over an algebraically closed field $\FF$ of characteristic coprime to $q$, and $H$ is a proper subgroup of…

We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…

In this paper we show how to construct, for most p >= 5, two types of surjective representations \rho:G_Q=Gal(\bar{Q}/Q) -> GL_2(Z_p) that are ramified at an infinite number of primes. The image of inertia at almost all of these primes will…

Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a quadratic extension. The aim of the present article is to study the multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$ occurring in an…

Let $G^{(r)}$ denote the metaplectic covering group of the linear algebraic group $G$. In this paper we study conditions on unramified representations of the group $G^{(r)}$ not to have a nonzero Whittaker function. We state a general…

Let $L/K$ be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of ${\rm Gal}(L/K)$, the sharper of which is conditional on the Artin Conjecture and the…

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

Let $\Ga$ be a connected, solvable linear algebraic group over a number field~$K$, let $S$ be a finite set of places of~$K$ that contains all the infinite places, and let $\theints$ be the ring of $S$-integers of~$K$. We define a certain…

By work of Belyi, the absolute Galois group $G_{\mathbb{Q}}=\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ of the field $\mathbb{Q}$ of rational numbers can be embedded into $A=\mathrm{Aut}(\widehat{F_2})$, the automorphism group of the…

A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…