Related papers: J-Groups of Lens Spaces modulo Odd Prime Powers
This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…
We make a computational study to know what kind of isospectralities among lens spaces and lens orbifolds exist considering the Hodge--Laplace operators acting on smooth $p$-forms. Several evidenced facts are proved and some others are…
We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles…
We develop JSJ decomposition theory of pro-p groups.
We consider the capability of $p$ groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition…
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
In this article, we determine all inequivalent irreducible rational matrix representations of groups of order $p^5$, where $p$ is an odd prime. We also derive combinatorial formulations for the Wedderburn decomposition of rational group…
In this paper, we compute the action of the mod $p$ Steenrod operations on the modular invariants of the linear groups with $p$ an odd prime number.
This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…
We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.
Cosmologists are taking a renewed interest in multiconnected spherical 3-manifolds (spherical spaceforms) as possible models for the physical universe. To understand the formation of large scale structures in such a universe, cosmologists…
Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory in the case when the fundamental group has order a power of $2$. As a corollary we also obtain a calculation of the…
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them…
Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matrix. We also obtain lower bounds on the size of such matrices…
In the first part of the paper we present a classification of fake lens spaces of dimension >= 5 whose fundamental group is the cyclic group of order N >= 2. The classification uses and extends the results of Wall and others in the case N =…
We note that a recent result of the second author yields upper bounds for odd-primary homotopy exponents of compact simple Lie groups which are often quite close to the lower bounds obtained from v_1-periodic homotopy theory.
We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of…
In this paper we describe the Jordan-Holder series of the standard modules over the rational Cherednik algebras associated with the dihedral group. In particular, we compute the characters of the irreducible representations from the…
Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure…