Related papers: An Ennola duality for subgroups of groups of Lie t…

The aim of this paper is to investigate Ennola duality for decomposition of tensor products of irreducible characters of finite general linear groups and finite unitary groups. We prove that Ennola duality holds generically and give a…

An enhanced algebraic group $\uG$ of $G=\GL(V)$ over $\bbc$ is a product variety $\GL(V)\times V$, endowed with an enhanced cross product. Associated with a natural tensor representation of $\uG$, there are naturally Levi and parabolic…

For uniform lattices $\Gamma$ in rank 1 Lie groups, we construct Anosov representations of virtual doubles of $\Gamma$ along certain quasiconvex subgroups. We also show that virtual HNN extensions of these lattices over some cyclic…

We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $\mathrm{L}\mathfrak{gl}_{M|N}=\mathbb{C}[t,t^{-1}]\otimes\mathfrak{gl}_{M|N}$ ($M\neq N$). We explain how…

It is well-known that every finite subgroup of GL_d(Q_{\ell}) is conjugate to a subgroup of GL_d(Z_{\ell}). However, this does not remain true if we replace general linear groups by symplectic groups. We say that G is a group of inertia…

We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in…

This is a successive paper of arXiv:1909.11492. We prove an equivalence between the category of finite-dimensional representations of degenerate supergroup $\underline{GL}(M|N)$ and the category of $(GL_M(O) \ltimes U_{M, N}(F), \chi_{M,…

Let $N(\Gamma,G)$ be the number of homomorphisms from $\Gamma$ to $G$ up to conjugation by $G$. Physics of four-dimensional $\mathcal{N}=4$ supersymmetric gauge theories predicts that $N(\Gamma,G)=N(\Gamma , \tilde G)$ when $\Gamma$ is a…

A pseudogroup is a complete infinitely distributive inverse monoid. Such inverse monoids bear the same relationship to classical pseudogroups of transformations as frames do to topological spaces. The goal of this paper is to develop the…

In this paper, we determine the modular invariants of finite modular pseudo-reflection subgroups of the finite general linear group $ \text{GL}_n(q) $ acting on the tensor product of the symmetric algebra $ S^{\bullet}(V) $ and the exterior…

Let $k$ be an algebraically closed field of characteristic $p>0$ and $G$ a finite group. We provide a description of the torsion subgroup $TT(G)$ of the finitely generated abelian group $T(G)$ of endo-trivial $kG$-modules when $p=2$ and $G$…

Let $G$ be a finite group such that $\text{SL}(n,q)\subseteq G \subseteq \text{GL}(n,q)$ and $Z$ be a central subgroup of $G$. In this paper we determine the group $T(G/Z)$ consisting of the equivalence classes of endotrivial…

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…

In the 80's Aschbacher classified the maximal subgroups of almost all of the finite almost simple classical groups. Essentially, this classification divide these subgroups into two types. The first of these consist roughly of subgroups that…

We prove part of a higher rank analogue of the Mazur-Gouvea Conjecture. More precisely, let $\tilde{\bf G}$ be a connected, reductive ${\Bbb Q}$-split group and let $\Gamma$ be an arithmetic subgroup of $\tilde{\bf G}$. We show that the…

This paper generalizes a theorem of Hida on the structure of ordinary representations on unitary groups to $P$-ordinary representations, where $P$ is a general parabolic subgroup of some general linear group. When $P$ is minimal, we recover…

Let $n\le 5$ be an integer, and let $\Gamma$ be a finite group. We prove that if $\rho , \rho': \Gamma \to O(n)$ are two representations that are conjugate by an orientation-preserving diffeomorphism, then they are conjugate by an element…

A quantum field theory with a finite abelian symmetry $G$ may be equipped with a non-invertible duality defect associated with gauging $G$. For certain $G$, duality defects admit an alternative construction where one starts with invertible…

Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point subgroup of GL(V). Motivated in parallel by questions in…