Related papers: Embedding central extensions of simple linear grou…

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer…

Let $G_{n,k}$ be the group of permutations of $\{1,2,\ldots, kn\}$ that permutes the first $k$ symbols arbitrarily, then the next $k$ symbols and so on through the last $k$ symbols. Finally the $n$ blocks of size $k$ are permuted in an…

Let $G$ be an irreducible imprimitive subgroup of $\operatorname{GL}_n(\mathbb{F})$, where $\mathbb{F}$ is a field. Any system of imprimitivity for $G$ can be refined to a nonrefinable system of imprimitivity, and we consider the question…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

We propose an unsupervised neural model for learning a discrete embedding of words. Unlike existing discrete embeddings, our binary embedding supports vector arithmetic operations similar to continuous embeddings. Our embedding represents…

Let G be a finite subgroup of SL(2,C). Let S_N#G^N be the wreath product of G by the symmetric group of degree N, acting symplectically on a complex vector space V of dimension 2N, with symplectic basis {x_i, y_i} i=1,...,N. In this paper…

We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order $n$. We compute the Plancherel measure of the representation using Eisenstein series and a comparison…

We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric…

A Gelafand model for wreath products $\Z_r\wr S_n$ is constructed. The proof relies on a combinatorial interpretation of the characters of the model, extending a classical result of Frobenius and Schur.

We present several multi-variable generating functions for a new pattern matching condition on the wreath product of the cyclic group and the symmetric group. Our new pattern matching condition requires that the underlying permutations…

The field of real numbers being extended as a larger commutative field, we investigate the possibility of defining a scalar product for the distributions of finite discrete support. Then we focus on the most simple possible extension (which…

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…

We prove Cherlin's conjecture, concerning binary primitive permutation groups, for those groups with socle isomorphic to $\mathrm{PSL}_2(q)$, ${^2\mathrm{B}_2}(q)$, ${^2\mathrm{G}_2}(q)$ or $\mathrm{PSU}_3(q)$. Our method uses the notion of…

For the unitary ensembles of $N\times N$ Hermitian matrices associated with a weight function $w$ there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For…

The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalised to discrete settings involving either a linear or exponential lattice. The corresponding correlation functions can be expressed…

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of the generalized…

We establish a central limit theorem for the central values of Dirichlet $L$-functions with respect to a weighted measure on the set of primitive characters modulo $q$ as $q \rightarrow \infty$. Under the Generalized Riemann Hypothesis…

We introduce the notion of central extension of gerbes on a topological space. We then show that there are obstruction classes to lifting objects and isomorphisms in a central extension. We also discuss pronilpotent gerbes. These results…

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…