Related papers: Reflection Groups and Differential Forms
Let $\mathcal{A} = \mathcal{A}(W)$ be the reflection arrangement of the finite complex reflection group $W$. By Terao's famous theorem, the arrangement $\mathcal{A}$ is free. In this paper we classify all reflection arrangements which…
Let V be an n-dimensional vector space and let On be the orthogonal group. Motivated by a question of B. Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society Volume 20, Number 4,…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…
To a complex reflection arrangement with an invariant multiplicity function one can relate the space of logarithmic vector fields and the space of quasi-invariants, which are both modules over invariant polynomials. We establish a close…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce the concept of convergence of the sequence of substitution…
In an earlier work, the author observed that Boolean inverse semi-groups, with semigroup homomorphisms preserving finite orthogonal joins, form a congruence-permutable variety of algebras, called biases. We give a full description of…
This paper is a contribution to Vinberg's theory of $\theta$-groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras. One of our main tools is Springer's theory of regular elements of finite reflection…
Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence…
We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…
In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
We investigate Seiberg-Witten theory in the presence of real structures. Certain conditions are obtained so that integer valued real Seiberg-Witten invariants can be defined. In general we study properties of the real Seiberg-Witten…
We give an invariant nondegeneracy condition for CR--maps between generic submanifolds in different dimensions and use it to prove a reflection principle for these maps.
We investigate feedback forms for linear time-invariant systems described by differential-algebraic equations. Feedback forms are representatives of certain equivalence classes. For example state space transformations, invertible…
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…