Related papers: Schur multipliers of unitriangular groups

A finite group $G$ is called a Schur group, if any Schur ring over $G$ is the transitivity module of a point stabilizer in a subgroup of $\sym(G)$ that contains all right translations. We complete a classification of abelian $2$-groups by…

Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…

We show that the nearring $(\mathbb{Z}[x],+,\circ)$ of integer polynomials, where the nearring multiplication is the composition of polynomials, has uncountably many subnearrings, and we give an explicit description of those nearrings that…

In this paper, we continue the enumeration of Schur rings over cyclic groups. Cyclic groups of semiprime order $pq$, where $p$ and $q$ are distinct primes, are considered. Additionally, cyclic groups of order $4p$ are considered.

Let $G$ be a group and $q$ a non-negative integer. We denote by $\nu^q(G)$ a certain extension of the $q$-tensor square $G \otimes^q G$ by $G \times G$. In this paper we derive a polycyclic presentation for $G \otimes^q G$, when $G$ is…

Schur's Theorem and its generalisation, Baer's Theorem, are distinguished results in group theory, connecting the upper central quotients with the lower central series. The aim of this paper is to generalise these results in two different…

Let $(\Omega_1, \mathcal{F}_1, \mu_1)$ and $(\Omega_2, \mathcal{F}_2, \mu_2)$ be two measure spaces and let $1 \leq p,q \leq +\infty$. We give a definition of Schur multipliers on $\mathcal{B}(L^p(\Omega_1), L^q(\Omega_2))$ which extends…

We establish a formula for the weight multiplicities of Demazure modules (in particular for highest weight representations) of a complex connected algebraic group in terms of the geometry of its Langlands dual.

In this paper we consider a general sequence of orthogonal Laurent polynomials on the unit circle and we first study the equivalences between recurrences for such families and Szego's recursion and the structure of the matrix representation…

We apply a theorem of Geronimus to derive some new formulas connecting Schur functions with orthogonal polynomials on the unit circle. The applications include the description of the associated measures and a short proof of Boyd's result…

We study the Schur polynomial expansion of a family of symmetric polynomials related to the refined enumeration of alternating sign matrices with respect to their inversion number, complementary inversion number and the position of the…

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…

We study the problem of characterizing Hankel-Schur multipliers and Toeplitz-Schur multipliers of Schatten-von Neumann class $\bS_p$ for $0<p<1$. We obtain various sharp necessary conditions and sufficient conditions for a Hankel matrix to…

We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive…

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

The generalized wreath product of permutation groups is introduced. By means of it we study the schurity problem for S-rings over a cyclic group $G$ and the automorphism groups of them. Criteria for the schurity and non-schurity of the…

We provide a bound on the dimension of Schur multiplier of a finite dimensional nilpotent Lie superalgebra which is more precise than the previous bounds on the dimension of Schur multiplier of Lie superalgebra.

In this paper, we introduce a family of Fourier multipliers using the spherical Fourier transform on Gelfand pairs. We refer to them as spherical Fourier multipliers. We study certain sufficient conditions under which they are bounded.…

A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite…

In a purely multi-variable setting (i.e., the issues discussed in this note are not interesting in the single variable operator theory setting), we show that the coincidence of two operator valued Schur class multipliers of a certain kind…