Abstract
In previous work Regev used part of the representation theory of Lie superalgebras to compute the values of a character of the symmetric group whose decomposition into irreducible constituents is described by semistandard (k, ℓ)-tableaux. In this short note we give a new proof of Regev’s result using skew characters.
Similar content being viewed by others
References
A. Berele and A. Regev, Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras, Adv. in Math. 64 (1987), 118–175.
G. James and A. Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, Vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981.
I. G. Macdonald, Symmetric functions and Hall polynomials, second ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995.
M. Novaes, Sum of skew characters over hooks and “odd” partitions, MathOverflow, Mar. 2016, http://mathoverflow.net/q/233009.
A. Regev, Lie superalgebras and some characters of S n, Israel J. Math. 195 (2013), 31–35.
Author information
Authors and Affiliations
Corresponding author
Additional information
The author gratefully acknowledges the financial support of an INdAM Marie-Curie Fellowship and grants CPDA125818/12 and 60A01-4222/15 of the University of Padova.
Rights and permissions
About this article
Cite this article
Taylor, J. A note on skew characters of symmetric groups. Isr. J. Math. 221, 435–443 (2017). https://doi.org/10.1007/s11856-017-1549-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11856-017-1549-0