Finiteness for the Wrt Representations of Mapping Class Groups
نویسندگان
چکیده
We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-Reshetikhin-Turaev TQFTs associated to SU(2) and SO(3) induce unitary representations of this group. We show these representations have finite image in the case r is an odd prime. We show this for all r if the surface is a sphere. We show this for all r if the surface is a torus and there are no colored points.
منابع مشابه
Bisimulation Collapse and the Process Taxonomy
We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA graphs (i.e. prefix transition graphs of context-free grammars) we can show that the factorization is e...
متن کاملGroups with Two Extreme Character Degrees and their Minimal Faithful Representations
for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...
متن کاملVanishing Resonance and Representations of Lie Algebras
We explore a relationship between the classical representation theory of a complex, semisimple Lie algebra g and the resonance varieties R(V,K) ⊂ V ∗ attached to irreducible g-modules V and submodules K ⊂ V ∧ V . In the process, we give a precise roots-and-weights criterion insuring the vanishing of these varieties, or, equivalently, the finiteness of certain modules W(V,K) over the symmetric a...
متن کاملThe Effect of Argument Mapping Instruction on L2 Writing Achievement across Writing Tasks and Writing Components: A Case of Iranian EFL Learners
Argument maps as schematic representations of arguments and their logical and evidential relationships are effective diagrams for instruction in education as well as in L2 development. However, their use for teaching L2 writing in EFL contexts has not been adequately studied. Therefore, this study investigated the effect of argument mapping instruction on Iranian EFL learners’ writing achieveme...
متن کامل2 9 Se p 20 04 ON THE ASYMPTOTICS OF QUANTUM SU ( 2 ) REPRESENTATIONS OF MAPPING CLASS GROUPS
We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In particular, they may be used to give an explicit check that spherical braid groups and hyperelliptic mapping class groups do not have Kazhdan’s property (T)....
متن کامل