On the TQFT representations of the mapping class groups

Louis Funar
1999 Pacific Journal of Mathematics  
We prove that the image of the mapping class group by the representations arising in the SU (2)-TQFT is infinite, provided that the genus g ≥ 2 and the level of the theory r = 2, 3, 4, 6 (and r = 10 for g = 2). In particular it follows that the quotient groups M g /N (t r ) by the normalizer of the r-th power of a Dehn twist t are infinite if g ≥ 3 and r = 2, 3, 4, 6, 8, 12. 2. Preliminaries. Hecke algebras and Temperley-Lieb algebras. We will outline briefly, for the sake of completeness, some
more » ... completeness, some basic notions concerning the Hecke algebras (see [49] for more details). Recall that the Hecke algebra of type A n−1 is the algebra over C generated by 1, g 1 , ..., g n−1 and the following relations: g i g i+1 g i = g i+1 g i g i+1 , i = 1, 2, ..., n − 2,
doi:10.2140/pjm.1999.188.251 fatcat:yhlfdsju7jdctaivfzycyffay4