Related papers: Brill's equations as a GL(V)-module

The main aim of this paper is the presentation of a new methodology to obtain Liouvillian solutions of stationary one dimensional Schr\"odinger equation with quasi-solvable polynomial potentials through the using of differential Galois…

Let $G$ be a cyclic group of order $p$, let $k$ be a field of characteristic $p$, and let $V, W$ be $kG$-modules. We study the modules of covariants $k[V,W]^G = (S(V^*) \otimes W)^G$. For $V$ indecomposable with dimension 2, and $W$ an…

We present an unconditional CRT algorithm to compute the modular polynomial $\Phi_\ell(X,Y)$ in quasi-linear time. The main ingredients of our algorithm are: the embedding of $\ell$-isogenies in smooth-degree isogenies in higher dimension,…

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g=3 into $ SL(2,C), and also of the moduli space of twisted representations. The case of genus g=1,2 has already been…

We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirming a conjecture of Leclerc and Thibon.

In this paper, we show the existence of a Chow--Kuenneth decomposition for the moduli stack of stable curves of genus g with r marked points, for low values of g,r. We also look at the moduli space R of double covers of genus 3 curves,…

We exploit the idea that the character of an irreducible finite dimensional $\mathfrak{gl}_n$-module is the sum of certain exponents of integer points in a Gelfand-Tsetlin polytope and can thus be calculated via Brion's theorem. In order to…

We give a closed formula for the graded decomposition numbers of the blob algebra over a field of characteristic zero at a root of unity.

This paper is the third and final part of a series devoted to the description of the integral Chow rings of the moduli stacks of hyperelliptic Prym pairs. For a fixed genus $g$, there are two natural stacks, $\mathcal{RH}_g$ and…

We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for the decomposition of multivariate exponential sums,…

Mahler equations relate evaluations of the same function $f$ at iterated $b$th powers of the variable. They arise in particular in the study of automatic sequences and in the complexity analysis of divide-and-conquer algorithms. Recently,…

We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split groups done by Kac to the non-split quasi-split case. For the…

Given a chiral algebra, we study modules over an arbitrary power of a curve. We describe this category in three different ways: in terms of factorization, in terms of certain chiral operations and as modules for a lie algebra in a certain…

We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule.…

Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in…

We compute the Chow groups of smooth Gushel-Mukai varieties of dimension $5$.

We investigate some Galois groups of linearized polynomials over fields such as $\mathbb{F}_q(t)$. The space of roots of such a polynomial is a module for its Galois group. We present a realization of the symmetric powers of this module, as…

We establish the existence of the Bernstein polynomial in one indeterminate $t$, and provide a method for its explicit computation. The Bernstein polynomial is associated with finitely generated modules over the Weyl algebra, known as…

We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…

Let $G$ be the product $GL_r(C) \times (C^\times)^n$. We show that the $G$-equivariant Chow class of a $G$ orbit closure in the space of $r$-by-$n$ matrices is determined by a matroid. To do this, we split the natural surjective map from…