Abstract
Let H be an extension of a finite group Q by a finite group G. Inspired by the results of duality theorems for étale gerbes on orbifolds, the authors describe the number of conjugacy classes of H that map to the same conjugacy class of Q. Furthermore, a generalization of the orthogonality relation between characters of G is proved.
Similar content being viewed by others
References
Behrend, K. and Xu, P., Differentiable stacks and gerbes, J. Symplectic Geom., 9(3), 2011, 285–341.
Berkovich, Y. G. and Zhmud’, E. M., Characters of Finite Groups, Part 1, Translations of Mathematical Monographs, 172, Amer. Math. Soc., Providence, RI, 1998.
Fulton, W. and Harris, J., Representation Theory, Readings in Mathematics, Graduate Texts in Mathematics, 129, Springer-Verlag, New York, 1991.
Hellerman, S., Henriques, A., Pantev, T., et al., Cluster decomposition, T-duality, and gerby CFTs, Adv. Theor. Math. Phys., 11(5), 2007, 751–818.
Laurent-Gengoux, C., Stiénon, M. and Xu, P., Non-abelian differentiable gerbes, Adv. Math., 220(5), 2009, 1357–1427.
Ruan, Y., Discrete torsion and twisted orbifold cohomology, J. Symplectic Geom., 2(1), 2003, 1–24.
Schreier, O., Uber die Erweiterung von Gruppen I, Monatsh. Math. Phys., 34(1), 1926, 165–180.
Tang, X. and Tseng, H. -H., Duality theorems for étale gerbes on orbifolds, Adv. Math., 250, 2014, 496–569.
Tu, J., Xu, P. and Laurent-Gengoux, C., Twisted K-theory of differentiable stacks, Ann. Sci.École Norm. Sup. (4), 37(6), 2004, 841–910.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Science Foundation (No. 0900985), the National Security Agency (No. H98230-13-1-0209), the National Science Foundation (No. DMS-0757722) and the Simons Foundation collaboration grant.
Rights and permissions
About this article
Cite this article
Tang, X., Tseng, HH. Conjugacy classes and characters for extensions of finite groups. Chin. Ann. Math. Ser. B 35, 743–750 (2014). https://doi.org/10.1007/s11401-014-0854-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11401-014-0854-8