Related papers: Representation of modular invariant function by ge…

We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid.

In our preceding article, we defined a generalized lambda function and showed that the genaralized lambda function and the modular invariant function generate the modular function field with respect to a principal congruence subgroup. In…

Let $G$ be a reductive group acting on a path algebra $kQ$ as automorphisms. We assume that $G$ admits a graded polynomial representation theory, and the action is polynomial. We describe the quiver $Q_G$ of the smash product algebra $kQ\#…

We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.

The purpose of this note is to find explicit representatives in deRham cohomology for the generators of the cohomology of the moduli space of parabolic bundles, analogous to the results of \cite{groupcoho} for the moduli space of vector…

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…

We show the modular properties of the multiple 'elliptic' gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's…

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

We present a constructive proof that all gauge invariant Lorentz scalars in Electrodynamics can be expressed as a function of the quadratic ones.

The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.

We present the general construction of the $U$-projector (the homomorphism of the algebra into its field of $U$-invariants identical on the subalgebra of $U$-invariants). It is shown how to apply $U$-projector to find the systems of free…

We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.

We describe several families of permutation polynomials obtained using functions with linear translators.

We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model $(V, G, \theta, w)$. We show that certain derivatives of $I$-functions of quasimap invariants of $[V //_\theta G]$ produce…

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…

For positive integers $g$ and $N$, let $\mathcal{F}_N$ be the field of meromorphic Siegel modular functions of genus $g$ and level $N$ whose Fourier coefficients belong to the $N$th cyclotomic field. We present explicit generators of…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

Let $F$ be a field of non-zero characteristic $p$, let $G$ be a cyclic group of order $q =p^a$ for some positive integer $a$, and let $U$ and $W$ be indecomposable $F G$-modules. We identify a generator for each of the indecomposable…

We prove a new formula for the generating function of polynomials counting absolutely stable representations of quivers over finite fields. The case of irreducible representations is studied in more detail.