Related papers: Cartesian symmetry classes associated with certain…

Let V be a unitary space. Suppose G is a subgroup of the full symmetric group S_m and X is an irreducible unitary representation of G. In this paper, we introduce the generalized Cartesian symmetry class over V associated with G and X. Then…

Let $(\mathfrak{g}, \mathfrak{k})$ be a complex quaternionic symmetric pair with $\mathfrak{k}$ having an ideal $\mathfrak{sl}(2, \mathbb{C})$, $\mathfrak{k}=\mathfrak{sl}(2, \mathbb{C})+\mathfrak{m}_c$. Consider the representation…

In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the…

For a pair $(G,G')=(O(n+1,1), O(n,1))$ of reductive groups, we investigate intertwining operators (symmetry breaking operators) between principal series representations $I_\delta(V,\lambda)$ of $G$, and $J_\epsilon(W,\nu)$ of the subgroup…

We reconsider an old problem, namely the dimension of the $G$-invariant subspace in $V^{\otimes p} \otimes V^{*\otimes q}$, where $G$ is one of the classical groups ${\rm GL}(V)$, ${\rm SL}(V)$, ${\rm O}(V)$, ${\rm SO}(V)$, or ${\rm…

We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigate them by means of tools from the representation theory of symmetric groups S_N such as…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…

Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…

Let $(\tilde Q,g) $ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V, \tilde{Q},g) \simeq (H^2 \otimes E^{2n}, \mathfrak{sl}(H),\omega^H \otimes \omega^E)$, we give an…

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…

*Caveat: we learned post-factum that most of these results are not novel. We are keeping this paper for continuity reasons.* Given finite-dimensional complex representations $V$ and $V'$ of a simply-connected semisimple compact Lie group…

We study the problem of finding generators for the fundamental group G of a space of the following sort: one removes a family of complex hyperplanes from n dimensional complex vector space, or n dimensional complex hyperbolic space, or the…

The orbit dimension $\sigma(G)$ (also called the separation number or rigidity index) of a permutation group $G$ with domain $\Omega$ is the minimum cardinality of a subset $S \subseteq \Omega$ such that, for any two distinct elements…

Let G be an infinite cyclic extension, 1 -> B -> G -> Z -> 1, of a group B where the action of Z on the set of conjugacy classes of non-trivial elements of B is free. This class of groups includes certain ascending HNN-extensions with…

A rational group of hermitian type is an algebraic group over the rational numbers whose symmetric space is a hermitian symmetric space. We assume such a group $G$ to be given, which we assume is isotropic. Then, for any rational parabolic…

Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…

Let G be a group acting isometrically with discrete orbits on a separable complete CAT(0)-space of bounded topological dimension. Under certain conditions, we give upper bounds for the Bredon cohomological dimension of G for the families of…

Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly…

Let \lambda be a partition of a positive integer n. Let C be a symmetric rigid tensor category over a field k of characteristic 0 or char(k)>n, and let V be an object of C. In our main result (Theorem 4.3) we introduce a finite set of…