相关论文: Reflection Groups and Differential Forms

Formal orbifolds are defined in higher dimension. Their \'etale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to…

We prove that the isomorphism problem for finitely generated fully residually free groups is decidable. We also show that each finitely generated fully residually free group G has a decomposition that is invariant under automorphisms of G,…

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…

We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…

We generalize the theory of logarithmic derivations through a self-contained study of modules here dubbed tangential idealizers. We establish reflexiveness criteria for such modules, provided the ring is a factorial domain. As a main…

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…

We construct an invariant of t-structures on the derived category of a Noetherian ring. This invariant is complete when restricting to the category of quasi-coherent complexes, and also gives a classification of nullity classes with the…

We introduce "continuous deformed preprojective algebras" attached to infinite affine Dynkin quivers of type A_{\infty}, A_{+\infty}, D_{\infty}. We define a one-parameter family of deformations of the wreath product of a symmetric group…

In this paper we introduce a new invariant (the distant degree) for difference field extensions of finite transcendence degree, and we explore some of its properties. We also discuss a generalisation of this invariant and of the limit…

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…

Using the set-up of deformation categories of Talpo and Vistoli, we re-interpret and generalize, in the context of cartesian morphisms in abstract categories, some results of Rim concerning obstructions against extensions of group actions…

A binding group theorem is proved in the context of quantifier-free internality to the fixed field in difference-closed fields of characteristic zero. This is articulated as a statement about the birational geometry of isotrivial algebraic…

We elucidate the key role played by formality in the theory of characteristic and resonance varieties. We show that the I-adic completion of the Alexander invariant of a 1-formal group G is determined solely by the cup-product map in low…

Drinfeld twists, and the twists of Giaquinto and Zhang, allow for algebras and their modules to be deformed by a cocycle. We prove general results about cocycle twists of algebra factorisations and induced representations and apply them to…

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…

In this paper we construct 16 free algebras of modular forms on symmetric domains of type IV for some reflection groups related to the eight lattices $A_1(2)$, $A_1(3)$, $A_1(4)$, $2A_1(2)$, $A_2(2)$, $A_2(3)$, $A_3(2)$, $D_4(2)$. As a…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

We give an intrinsic criterion to tell whether a reflection factorization in the general linear group is reduced, and give a formula for computing reflection length in the general affine group.

We introduce the notion of reflections for selfinjective algebras from the point of view of torsion theories induced by two-term tilting complexes. As an application, we determine the transformations of Brauer trees associated with…

We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…