IJAM: Volume 37, No. 5 (2024)

DOI: 10.12732/ijam.v37i5.4

IRREDUCIBLE REPRESENTATIONS

OF THE GROUP OF CONJUGATING

AUTOMORPHISMS OF A FREE GROUP

Mohamad N. Nasser 1, Rayane G. Abou Nasser Al Yaf 2,

Mohammad N. Abdulrahim 3,§

1,2,3 Department of Mathematics and Computer Science

Beirut Arab University

P.O. Box 11-5020, Beirut, LEBANON

Abstract. As E. Formanek has characterized low dimensional representations of the braid group

Bn, we extend these representations to the group of conjugating automorphisms Cn, when n \geq 5. We then give a classification for irreducible representations of Cn in dimensions of at most

n-3. Next, we determine representations of Cn in dimension n-1 when each of the restrictions to the symmetric group Sn and the braid group Bn are irreducible.

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How to cite this paper?
DOI: 10.12732/ijam.v37i5.4
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 5

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