Related papers: A survey on mapping class group representations de…
We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.
This is a survey on stated skein algebras and their representations.
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…
This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
We define an action of Artin's braid group on a finite dimensional algebra.
We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.
We describe an explicit finite presentation for a finite depth subfactor planar algebra. We also show that such planar algebras are singly generated with the generator subject to finitely many relations.
We give generators and relations for the planar algebras corresponding to $ADE$ subfactors. We also give a basis and an algorithm to express an arbitrary diagram as a linear combination of these basis diagrams.
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.
We provide an (almost) self-contained construction of the Witten-Reshetikhin-Turaev representations of the mapping class group. We describe its properties including its Hermitian structure, irreducibility and integrality (at prime level).…
We survey recent developments on mapping class groups of surfaces of infinite topological type.