Related papers: Discrete complex reflection groups
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
This is an edited write-up of lecture notes of the 7-th Appalachian set theory workshop of the same title led by the first named author at the Cornell University on November 22, 2008. A draft version of the notes was prepared by the second…
In this expanded account of a talk given at the Oberwolfach Arbeitsgemeinschaft "Totally Disconnected Groups", October 2014, we discuss results of Nikolay Nikolov and Dan Segal on abstract quotients of compact Hausdorff topological groups,…
We obtain a classification of discrete series representations of odd general spin groups, generalizing the M{\oe}glin-Tadi\'c classification for classical groups. Using mostly algebraic methods, available in both classical and the odd…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and postgraduate students of Novosibirsk State University and…
This survey is about combinatorial objects related to reflection groups and their applications in representation theory and arithmetic geometry. Coxeter groups and folded galleries in Coxeter complexes are introduced in detail and…
We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the…
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…
This is the announcement and partly the review of our results about classification of Lorentzian Kac-Moody algebras of the rank three. One of our results gives the classification of Lorentzian Kac-Moody algebras with denominator identity…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
It is shown that, under mild conditions, a complex reflection group $G(r,p,n)$ may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and a corresponding Hilbert…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…
Text of a (pre-dinner) lecture at the Bielefeld workshop "Discrete Categories in Representation Theory", April 20 - 21, 2018. This workshop was organized in order to celebrate the 60th birthday of Dieter Vossieck: his famous paper "The…
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
Discrete derived categories were studied initially by Vossieck and later by Bobi\'nski, Gei\ss, Skowro\'nski. In this article, we describe the homomorphism hammocks and autoequivalences on these categories. We classify silting objects and…
Talk given at the First Workshop on Forward Physics and Luminosity Determination at the LHC, Helsinki, Finland, November 2000. 12 pages, 9 figures
We study affine group schemes over a discrete valuation ring $R$ using two techniques: Neron blowups and Tannakian categories. We employ the theory developed to define and study differential Galois groups of $\mathcal D$-modules on a scheme…
These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group…