Related papers: A survey on mapping class group representations de…
Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…
Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroids. The support of a representable class can be (partially)…
We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Especially, for a Dynkin quiver, we establish a bijection…
We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…
We give a survey of the theory of surface braid groups and the lower algebraic K-theory of their group rings. We recall several definitions and describe various properties of surface braid groups, such as the existence of torsion,…
In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their…
Inspired by the reconstruction program of conformal field theories of Vaughan Jones we recently introduced a vast class of so called forest-skein groups. They are built from a skein presentation: a set of colours and a set of pairs of…
We give an infinite presentation for the mapping class group of a non-orientable surface. The generating set consists of all Dehn twists and all crosscap pushing maps along simple loops.
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
This is a survey article describing the various ways in which the Kauffman bracket skein module is a quantization of surface group characters. These include a purely heuristic sense of deformation of a presentation, a Poisson quantization,…
The modular representation theory of finite groups has its origins in the work of Richard Brauer. In this survey article we first discuss the work being done on some outstanding conjectures in the theory. We then describe work done in the…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
We compute explicitly up to Morita-equivalence the skew group algebra of a finite group acting on the path algebra of a quiver and the skew group algebra of a finite group acting on a preprojective algebra. These results generalize previous…