Related papers: Symmetric polynomials over finite fields
In this paper, we investigate some new symmetric identities for the q-Euler polynomials under the symmetric group of degree n which are derived from fermionic p-adic q-integrals on Zp.
We study covering graphs of the Paley graph associated to a finite field of characteristic p in the case where the covering transformation group is cyclic of prime order distinct from p. When the field has q = p elements, we show that the…
We consider properties of polynomials with coefficients in division rings. A theorem on the decomposition of a polynomial with coefficients in an arbitrary division ring is obtained. It is shown that if a non-central element is not a root…
Motivated by analogous results for the symmetric group and compact Lie groups, we study the distribution of the number of fixed vectors of a random element of a finite classical group. We determine the limiting moments of these…
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…
The endomorphism algebras of the permutation modules for transitive permutation groups, known as Hecke algebras, are fundamental objects in representation theory. While group algebras are known to be symmetric over any field, it is natural…
We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…
Let F be the field of two elements and G a finite abelian 2-group with an involutory automorphism. The extension of this automorphism to the group algebra FG is called an involutory involution. This determines the groups of unitary and…
Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric…
Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
We study the combinatorial types of periodic orbits of the standard covering endomorphisms ${\mathbf m}_k(x)=k x \ (\text{mod} \ {\mathbb Z})$ of the circle for integers $k \geq 2$ and the frequency with which they occur. For any $q$-cycle…
Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full…
We prove that certain acyclic cluster algebras over the complex numbers are the coordinate rings of holomorphic symplectic manifolds. We also show that the corresponding quantum cluster algebras have no non-trivial prime ideals. This allows…
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.
We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially…
In [GTZ08, GTZ12], the following result was established: given polynomials $f,g\in\mathbb{C}[x]$ of degrees larger than $1$, if there exist $\alpha,\beta\in\mathbb{C}$ such that their corresponding orbits $\mathcal{O}_f(\alpha)$ and…
The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…