Related papers: The Benson-Symonds Invariant for Permutation Modul…

We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…

In this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign, to each locally compact quantum group $\mathbb{G}$, a locally compact group $\tilde \mathbb{G}$ which is the quantum…

We use the variety of one-parameter subgroups to define a numerical invariant for a representation of an infinitesimal group scheme. For an indecomposable module M of complexity 1, this number is related to the period of M.

Let $\gamma$ be a filling curve on a topological surface $\Sigma$ of genus $g \geq 2$. The inf invariant of $\gamma$, denoted $m_{\gamma}$, is the infimum of the length function on the space of marked hyperbolic structures on $\Sigma$. This…

Since any string theory involves a path integration on the world-sheet metric, their partition functions are volume forms on the moduli space of genus g Riemann surfaces M_g, or on its super analog. It is well known that modular invariance…

We consider the category of finite dimensional representations of the quantum double of a finite group as a modular tensor category. We study auto-equivalences of this category whose induced permutations on the set of simple objects…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

In this paper, we compute the {\Sigma}^n(G) and {\Omega}^n(G) invariants when 1 \rightarrow H \rightarrow G \rightarrow K \rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions…

Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \…

Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on the manifold $M$ by diffeomorphisms one can define the $\Gamma$-co-invariant cohomology of $M$ to be the cohomology of the differential complex…

We define an invariant \beta(M) of a finite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. \beta(M) lies in a subgroup of \B(\C) of…

In a series of papers the authors associated to an $L^2$-acyclic group $\Gamma$ an invariant $\mathcal{P}(\Gamma)$ that is a formal difference of polytopes in the vector space $H_1(\Gamma;\Bbb{R})$. This invariant is in particular defined…

We propose to construct the finite modular groups from the quotient of two principal congruence subgroups as $\Gamma(N')/\Gamma(N")$, and the modular group $SL(2,\mathbb{Z})$ is extended to a principal congruence subgroup $\Gamma(N')$. The…

If $\mathbb{F}_{q}$ is a finite field, $C$ is a vector subspace of $\mathbb{F}_{q}^{n}$ (linear code), and $G$ is a subgroup of the group of linear automorphisms of $\mathbb{F}_{q}^{n}$, $C$ is said to be $G$-invariant if $g(C)=C$ for all…

In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this…

In this paper, we study quantum modular forms in connection to quantum invariants of plumbed 3-manifolds introduced recently by Gukov, Pei, Putrov, and Vafa. We explicitly compute these invariants for any $3$-leg star plumbing graphs whose…

We determine all the terms that are gauge-invariant up to a total spacetime derivative ("semi-invariant terms") for gauged non-linear sigma models. Assuming that the isotropy subgroup $H$ of the gauge group is compact or semi-simple, we…

Let $\Omega=\{1,2,...,n\}$ where $n \ge 2$. The {\em shape} of an ordered set partition $P=(P_1,..., P_k)$ of $\Omega$ is the integer partition $\lambda=(\lambda_1,...,\lambda_k)$ defined by $\lambda_i = |P_i|$. Let G be a group of…

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…