Related papers: Non-Induced Representations of Finite Cyclic Group…

In the paper we show that any irreducible representation of a finitely generated nilpotent group $G$ over a finitely generated field $F$ of characteristic zero is induced from a primitive representation of some subgroup of $G$.

Let $\mathbb{F}_q$ be the finite field with $q$ elements, $F:=\mathbb{F}_q(T)$ and $F^{\operatorname{sep}}$ a separable closure of $F$. Set $A$ to denote the polynomial ring $\mathbb{F}_q[T]$. Let $\mathfrak{p}$ be a non-zero prime ideal of…

We study the representations of the commutator subgroup K_{n} of the braid group B_{n} into a finite group . This is done through a symbolic dynamical system. Some experimental results enable us to compute the number of subgroups of K_{n}…

The induced representation ${\rm Ind}_H^GS$ of a locally compact group $G$ is the unitary representation of the group $G$ associated with unitary representation $S:H\rightarrow U(V)$ of a subgroup $H$ of the group $G$. Our aim is to develop…

We give an explicit algebraic description, based on prismatic cohomology, of the algebraic K-groups of rings of the form $O_K/I$ where $K$ is a p-adic field and $I$ is a non-trivial ideal in the ring of integers $O_K$; this class includes…

The first part of this article is devoted to characterizing the cocycles $\alpha$ of a finite group $G$ that give rise to faithful projective representations of $G$. We prove that a $p$-group $G$ admits a faithful irreducible projective…

We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a reductive algebraic group G defined and split over a non-archimedean local field K. Following their lines, we prove that the generalized Steinberg representations of G…

Let $A$ be a commutative noetherian ring and $I$ an ideal in $A$. We characterize algebraically when all the minimal primes of the associated graded ring $G_I A$ contract to minimal primes of $A/I$. This, applied to intersection theory,…

We fix a field $\kk$ of characteristic $p$. For a finite group $G$ denote by $\delta(G)$ and $\sigma(G)$ respectively the minimal number $d$, such that for any finite dimensional representation $V$ of $G$ over $\kk$ and any $v\in…

We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B}…

We determine the structure of the weak*-closed $G$-invariant ideals in the Fourier-Stieltjes algebra $B(G)$ of certain groups $G$ by means of a $K$-theoretical obstruction. The groups to which this applies are groups whose only irreducible…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

Let G be a finite abelian group. A number field K is called a Hilbert-Speiser field of type G if for every tame G-Galois extension L/K has a normal integral basis, i.e., the ring of integers O_L is free as an O_K[G]-module. Let C_p denote…

Let $R$ be a polynomial ring in $N$ variables over an arbitrary field $K$ and let $I$ be an ideal of $R$ generated by $n$ polynomials of degree at most 2. We show that there is a bound on the projective dimension of $R/I$ that depends only…

In this paper we establish a formal connection between the structure of ideals in integers rings and the theory of additive combinatorics. For integers rings with cyclic class groups, we prove a structural theorem demonstrating that every…

We prove the following result related to the inverse problem for universal deformation rings of group representations: Given a finite field k, denote by W(k) the ring of Witt vectors over k and by K the field of fractions of W(k). If a…

Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H<G$ and $\mathbb{F} G$-modules $L$ such that the restriction…

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…

The notion of a glider representation of a chain of normal subgroups of a group is defined by a new structure, i.e. a fragment for a suitable filtration on the group ring. This is a special case of general glider representations defined for…

If G is a finitely generated group, and A an algebraic group, then Hom(G,A) is a possibly reducible algebraic variety denoted by R_A(G). Here we define the profile function, P_d(R_A(G)), of the representation variety of G over A to be…