Related papers: Discrete complex reflection groups
In this paper we study the category of discrete G-spectra for a profinite group G. We consider an embedding of module objects in spectra into a category of module objects in discrete G-spectra, and study the relationship between the…
In this work, we introduce a class of Timmermann's measured multiplier Hopf *-algebroids called algebraic quantum transformation groupoids of compact type. Each object in this class admits a Pontrjagin-like dual called an algebraic quantum…
These are notes (in Dutch) of lectures on multiple scattering of waves, given at the University of Amsterdam in 1993. At request of some of the students, now professors, they are made publicly available. The main part of the material is…
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…
We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
Nonabelian discrete groups are an attractive tool to describe fermion masses and mixings. They have nonsinglet representations which seem particularly suitable for distinguishing the lighter generations from the heavier ones. Also, they do…
An interesting question is whether two 3-manifolds can be distinguished by computing and comparing their collections of finite covers; more precisely, by the profinite completions of their fundamental groups. In this paper, we solve this…
Derived categories were invented by Grothendieck and Verdier around 1960, not very long after the "old" homological algebra (of derived functors between abelian categories) was established. This "new" homological algebra, of derived…
We give an introduction to the structure theory of extended affine Lie algebras, which provide a common framework for finite-dimensional semisimple, affine and toroidal Lie algebras. The notes are based on a lecture series given during the…
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
In this paper, we review the properties and representations of the Weyl groups relevant in the study of discrete integrable systems. Previously in \cite{jns4, Shi:19}, properties of Weyl groups of type $ADE$ (known as simply-laced) were…
In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…
We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…
We review recent progress on the modeling and use of reflection spectra from irradiated and ionized accretion discs. On the computational side, calculations of reflection spectra from discs with non-uniform density structure have shown that…
These are notes for lectures given at MIT in 1999 (Fall). They contain a discussion of affine Hecke algebras with possibly unequal parameters including a theory of cells and a partly conjectural theory of J-rings.
We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…
We give a geometric description of a certain class of epimorphisms between complex reflection groups. We classify these epimorphisms, which can be interpreted as ``morphisms'' between the diagrams symbolizing standard presentations by…
Lecture notes for the minicourse "Holonomy Groups in Riemannian geometry", a part of the XVII Brazilian School of Geometry, to be held at UFAM (Amazonas, Brazil), in July of 2012.
This article is an extended version of the talk given by the author in the seminar Th\'eorie Spectrale et G\'eom\'etrie at the Institut Fourier in March 2022. We present some results from the author's doctoral thesis, extended by several…