Related papers: Free reflection multiarrangements and quasi-invari…
We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular…
Classical invariant theory of a complex reflection group $W$ highlights three beautiful structures: -- the $W$-invariant polynomials constitute a polynomial algebra, over which -- the $W$-invariant differential forms with polynomial…
Given a finite residue field $k$, one looks for a smoothness basis that is invariant under the automorphism group of $k$. We construct models for some finite fields that admit such a basis. This work aims at accelerating algorithms for…
We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by…
If $\rho$ denotes a finite dimensional complex representation of $\textbf{SL}_2(\textbf{Z})$, then it is known that the module $M(\rho)$ of vector valued modular forms for $\rho$ is free and of finite rank over the ring $M$ of scalar…
Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a…
In this note we study the freeness of the module of derivations on all moduli of the $X_3$ arrangement with multiplicities. We use homological techniques stemming from work of Yuzvinsky, Brandt, and Terao which have recently been developed…
In this note we settle some technical questions concerning finite rank quasi-free Hilbert modules and develop some useful machinery. In particular, we provide a method for determining when two such modules are unitarily equivalent. Along…
In this paper, we study inequalities involving polynomials and quasimodular forms. More precisely, we focus on the monotonicity of the functions of the form $t \mapsto t^m F(it)$ where $F$ is a quasimodular form and $m > 0$. As an…
We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…
We investigate a class of non-quasi-homogeneous free divisors in the sense of Saito. These divisors are defined by equations of the form $D:= \{h=0\}$ on $\mathbb{C}^p$, where the polynomial $h$ is specific linear combination of monomials…
We generalize the rotationally-invariant formulation of the slave-boson formalism to multiorbital models, with arbitrary interactions, crystal fields, and multiplet structure. This allows for the study of multiplet effects on the nature of…
Suppose that W is a finite, unitary reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. There is the stronger…
We provide a general construction procedure for antilinearly invariant complex root spaces. The proposed method is generic and may be applied to any Weyl group allowing to take any element of the group as a starting point for the…
Suppose that W is a finite, unitary, reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. Let L(A) be the…
It is shown that the description of certain class of representations of the holonomy Lie algebra associated to hyperplane arrangement $\Delta$ is essentially equivalent to the classification of $\vee$-systems associated to $\Delta.$ The…
We introduce a weighted version of the module of logarithmic derivations of a divisor in weighted projective space, and provide a generalization of Saito's criterion for freeness in terms of weighted multiple eigenschemes (wME-schemes).…
First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…
We study the space of multilinear invariants \( V_f \) of degree \( f \) for a specified finite unitary reflection group. A subspace \( W_f \) of typical invariants is also introduced. We note that the dimension of \( W_f \) is given by…
This article is a sequel of [4], where we introduced quadratic forms on a module~ $V$ over a supertropical semiring $R$ and analysed the set of bilinear companions of a quadratic form $q: V \to R$ in case that the module $V$ is free, with…