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On Complex Characters of SL(4,q)

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 1998-1999
Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper we restricted the complex characters of GL(4,q) down to SL(4,q) by using the character values on classes of GL(4,q). Using a version of Clifford's Theorem making use of properties of roots of unity, we determine which restricted characters are irreducible, which of them are split and how many parts they split up into irreducible components. Thus, we determine some of irreducible complex characters of SL{4,q) and degrees of conjugate irreducible components of all reducible restricted characters.
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FULL TEXT (PDF): 
PDF icon arastrmx_190866_57-58_pp_163-213.pdf
163-213
  • English

REFERENCES

References: 

[I] Dickson. L.L.; Linear Groups. Dover. New York, 1958.
[2] Dornhoff.
L
; Group Representation Theory (Part A), Dekker, New York. 1971.
[3) Green. J.A.; The Characters of The f inite General Linear Groups. Trans. Amer. Math.Soc. 80 (1955), 402-477.
[4] Isaacs. LIVL: Character Theory of finite Groups. Academic Press, New York-London, 1976.
[5] Little wood^ D.H.; The Theory of Group Characters and Matrix Representations of Groups, Oxford. 1940.
[6] Simpson W.A. and frame, J.S.; The Character Tables for SL(3.q). SU(3.q2), PSL(3.q), PSU(3.q2), Can.J Math, vol 25. No. 3 (1973). 486¬494.
[7] Steinberg, R.; The Representation of GL(3.q). GL(4,q), PGL(3.q) and PGL(4,q), Can. J. Math. 3 (1951). 225-235.

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