Nazarov’s construction of the ordinary irreducible projective matrix representations of the symmetric group, an application of SYMMETRICA. (English) Zbl 0819.20011
In 1988, M. L. Nazarov [Funkts. Anal. Prilozh. 22, 77-78 (1988; Zbl 0658.20010)] announced his ingenious explicit construction of the irreducible projective representations of symmetric groups. The details appeared later [J. Lond. Math. Soc., II. Ser. 42, 437-451 (1990; Zbl 0677.20011)]. This construction should be compared with the classical construction of the semi-normal and orthogonal form in the ordinary case due to A. Young. The present paper gives a detailed description of this construction. Furthermore, the author gives an account of her implementation of this construction in the computer algebra system SYMMETRICA which has been developed at the University of Bayreuth. This should prove to be useful for those who need to work explicitly with these representations.
Reviewer: A.O.Morris (Aberystwyth)
MSC:
| 20C30 | Representations of finite symmetric groups |
| 20C25 | Projective representations and multipliers |
| 20C40 | Computational methods (representations of groups) (MSC2010) |
