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July, 2003 Nonexistence of modular fusion algebras whose kernels are certain noncongruence subgroups
Makoto TAGAMI
J. Math. Soc. Japan 55(3): 681-693 (July, 2003). DOI: 10.2969/jmsj/1191418997

Abstract

A well-known conjecture states that the kernel of representation associated to a modular fusion algebra is always a congruence subgroup. Assuming this conjecture, Eholzer studied modular fusion algebras such that the kernel of representation associated to each of them is a congruence subgroup using the fact that all irreducible representaions of SL(2,Z/pλZ) are classified. He classified all strongly modular fusion algebras of dimension two, three, four and the nondegenerate ones with dimension 24. In this paper, we try to imitate Eholzer's work. We classify modular fusion algebras such that the kernel of representation associated to each of them is a noncongruence normal subgroup of Γ:=PSL(2,Z) containing an element (1601). Among such normal subgroups, there exist infinitely many noncongruence subgroups. In a sense, they are the classes of near congruence subgroups. For such a normal subgroup G, we shall show that any irreducible representation of degree not equal to 1 of Γ/G is not associated to a modular fusion algebra.

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Makoto TAGAMI. "Nonexistence of modular fusion algebras whose kernels are certain noncongruence subgroups." J. Math. Soc. Japan 55 (3) 681 - 693, July, 2003. https://doi.org/10.2969/jmsj/1191418997

Information

Published: July, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1048.11033
MathSciNet: MR1978217
Digital Object Identifier: 10.2969/jmsj/1191418997

Subjects:
Primary: 05E99
Secondary: 11F06

Keywords: admissible , fusion algebra , little group method , modular fusion algebra , non congruence subgroup , nondegenerate

Rights: Copyright © 2003 Mathematical Society of Japan

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Vol.55 • No. 3 • July, 2003
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