Irreducible projective characters of wreath products
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- by Xiaoli Hu and Naihuan Jing
- Proc. Amer. Math. Soc. 143 (2015), 1015-1026
- DOI: https://doi.org/10.1090/S0002-9939-2014-12343-4
- Published electronically: November 3, 2014
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Abstract:
The irreducible character values of the spin wreath products $\widetilde {\Gamma }_n=\Gamma \wr \widetilde {S}_n$ of the symmetric group and a finite group $\Gamma$ are completely determined for arbitrary $\Gamma$.References
- Igor B. Frenkel, Naihuan Jing, and Weiqiang Wang, Twisted vertex representations via spin groups and the McKay correspondence, Duke Math. J. 111 (2002), no. 1, 51–96. MR 1876441, DOI 10.1215/S0012-7094-02-11112-0
- Peter N. Hoffman and John F. Humphreys, Hopf algebras and projective representations of $G\wr S_n$ and $G\wr A_n$, Canad. J. Math. 38 (1986), no. 6, 1380–1458. MR 873418, DOI 10.4153/CJM-1986-070-1
- X. Hu and N. Jing, Spin characters of generalized symmetric groups, Monatsh. Math. 173 (2014), 495-518. doi:10.1007/s00605-013-0525-y.
- Nai Huan Jing, Vertex operators, symmetric functions, and the spin group $\Gamma _n$, J. Algebra 138 (1991), no. 2, 340–398. MR 1102815, DOI 10.1016/0021-8693(91)90177-A
- Tadeusz Józefiak, A class of projective representations of hyperoctahedral groups and Schur $Q$-functions, Topics in algebra, Part 2 (Warsaw, 1988) Banach Center Publ., vol. 26, PWN, Warsaw, 1990, pp. 317–326. MR 1171281
- I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144
- A. O. Morris, The spin representation of the symmetric group, Proc. London Math. Soc. (3) 12 (1962), 55–76. MR 136668, DOI 10.1112/plms/s3-12.1.55
- Alun O. Morris and Huw I. Jones, Projective representations of generalized symmetric groups, Sém. Lothar. Combin. 50 (2003/04), Art. B50b, 27. MR 2049553
- Maxim Nazarov, Young’s symmetrizers for projective representations of the symmetric group, Adv. Math. 127 (1997), no. 2, 190–257. MR 1448714, DOI 10.1006/aima.1997.1621
- E. W. Read, The $\alpha$-regular classes of the generalized symmetric group, Glasgow Math. J. 17 (1976), no. 2, 144–150. MR 412267, DOI 10.1017/S0017089500002871
- I. Schur, Über die Darstellung der symmertrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 139 (1911), 155–250.
- Jean-Pierre Serre, Représentations linéaires des groupes finis, Third revised edition, Hermann, Paris, 1978 (French). MR 543841
- W. Specht, Eine Verallgemeinerung der symmetrischen Gruppen, Schriffen Math. Sem. Berlin 1 (1932), 1–32.
- David B. Wales, Some projective representations of $S_{n}$, J. Algebra 61 (1979), no. 1, 37–57. MR 554850, DOI 10.1016/0021-8693(79)90304-1
Bibliographic Information
- Xiaoli Hu
- Affiliation: School of Mathematics and Computer Science, Jianghan University, Wuhan 430056, People’s Republic of China
- Email: xiaolihumath@163.com
- Naihuan Jing
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- MR Author ID: 232836
- Email: jing@math.ncsu.edu
- Received by editor(s): February 1, 2013
- Received by editor(s) in revised form: June 3, 2013, June 4, 2013, and July 9, 2013
- Published electronically: November 3, 2014
- Communicated by: Pham Huu Tiep
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 1015-1026
- MSC (2010): Primary 20C25; Secondary 20C30, 20E22
- DOI: https://doi.org/10.1090/S0002-9939-2014-12343-4
- MathSciNet review: 3293719