相关论文: Orbits of $Z \circ (2.O_8^+(2).2)$ in Dimension 8

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V^G is regular. It is proved that every irreducible V^G-module occurs in an irreducible g-twisted V-module for some g in G. Moreover, the quantum…

Langlands has introduced a formula for a specific product of orbital integrals in $\mbox{GL}(2, \mathbb{Q})$. Altu\u{g} employs this formula to manipulate the regular elliptic part of the trace formula, with the aim of eliminating the…

We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms $F,G$ for orthogonal groups of signature $(2,n+2)$. In the case when $F$ is a Hecke eigenform and $G$ is a Maass lift of a Poincar\'e series, we…

Suppose that $G$ is a finite solvable group and $V$ is a finite, faithful and completely reducible $G$-module. Let $N$ be a nilpotent subgroup of $G$, then there exits $v \in V$ such that $|\bC_N(v)| \leq (|N|/p)^{1/p}$, where $p$ is the…

Algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real or quaternionic structure, it is natural to ask for the properties of the groups of real or…

We study orbits in a family of Markoff-like surfaces with extra off-diagonal terms over prime fields $\mathbb{F}_p$. It is shown that, for a typical surface of this form, every non-trivial orbit has size divisible by $p$. This extends a…

This is the author's second paper treating the double coset problem for classical groups. Let $G$ be an algebraic group over an algebraically closed field $K$. The double coset problem consists of classifying the pairs $H,J$ of closed…

We characterise finite groups such that for an odd prime $p$ all the irreducible characters in its principal $p$-block have odd degree. We show that this situation does not occur in non-abelian simple groups of order divisible by $p$ unless…

We study problems relating to the D(2)-Problem for metacyclic groups of type $G(p,p-1)$ where $p$ is an odd prime. Specifically we build on Nadim's thesis \cite{Jamil}, which showed that the $\mathbb{Z}[G(5,4)]$-module $\mathbb{Z}$ admits a…

Colmez has given a recipe to associate a smooth modular representation Omega(W) of the Borel subgroup of GL_2(Q_p) to a F_p^bar-representation W of Gal(Qp^bar/Qp) by using Fontaine's theory of (phi,Gamma)-modules. We compute Omega(W)…

Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group G_S(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical…

Fix a module M over a local ring R and a group action G on M, not necessarily R-linear. To understand how large is the G-orbit of an element z\in M one looks for the large submodules of M lying in Gz. We provide the corresponding…

Let $\mathbb{F}_q$ be a finite field with $q$ elements, where $q$ is the power of an odd prime, and let $\mathrm{GSp}(2n, \mathbb{F}_q)$ and $\mathrm{GO}^{\pm}(2n, \mathbb{F}_q)$ denote the symplectic and orthogonal groups of similitudes…

For $G$ a connected, reductive group over an algebraically closed field $k$ of large characteristic, we use the canonical Springer isomorphism between the nilpotent variety of $\mathfrak{g}:=\mathrm{Lie}(G)$ and the unipotent variety of $G$…

Let $\mathfrak{o}$ be a complete discrete valuation ring with finide residue field $\mathsf{k}$ of odd characteristic, and let $\mathbf{G}$ be a symplectic or special orthogonal group scheme over $\mathfrak{o}$. For any $\ell\in\mathbb{N}$…

Let $G=\mathrm{GL}_n(\mathbb{F})$, $\mathrm{O}_n(\mathbb{F})$, or $\mathrm{Sp}_{2n}(\mathbb{F})$ be one of the classical groups over an algebraically closed field $\mathbb{F}$ of characteristic $0$, let $\breve{G}$ be the MVW-extension of…

In the representation theory of split reductive algebraic groups, it is well known that every Weyl module with minuscule highest weight is irreducible over every field. Also, the adjoint representation of $E_8$ is also irreducible over…

Consider the semisimple mod p reduction of the Galois representation associated to a Hilbert newform f by Carayol and Taylor. This paper discusses how, under certain conditions on f, the universal ring for deformations of this residual…

In the present paper we indicate some Leibniz algebras whose closures of orbits under the natural action of $\GL_n$ form an irreducible component of the variety of complex $n$-dimensional Leibniz algebras. Moreover, for these algebras we…

In this paper we answer a question of Gabriel Navarro about orbit sizes of a finite linear group H acting completely reducibly on a vector space V: if the orbits containing the vectors a and b have coprime lengths m and n, we prove that the…