Linear Representations of Hyperelliptic Mapping Class Groups
نویسندگان
چکیده
منابع مشابه
Reducibility of quantum representations of mapping class groups
In this paper we provide a general condition for the reducibility of the ReshetikhinTuraev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are redu...
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We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-ReshetikhinTuraev TQFTs associated to SU(2) and SO(3) induce linear representations of this group. We show that the denominators of matrices which describe these representations over a cyclotomic field can be restricted in many cases. In this way, we give a proof of the...
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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 i...
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In [9] the author proved that in characteristic 0 the jacobian J(C) = J(Cf ) of a hyperelliptic curve C = Cf : y 2 = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f ∈ K[x] is “very big”. Namely, if n = deg(f) ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then the ring ...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2021
ISSN: 0026-2285
DOI: 10.1307/mmj/20195783