×

zbMATH — the first resource for mathematics

A character relationship between symmetric group and hyperoctahedral group. (English) Zbl 07304867
Summary: We relate the character theory of the symmetric groups \(\mathbb{S}_{2 n}\) and \(\mathbb{S}_{2 n + 1}\) with that of the hyperoctahedral group \(\mathbb{B}_n=(\mathbb{Z}/2)^n\rtimes \mathbb{S}_n\), as part of the expectation that the character theory of reductive groups with diagram automorphism and their Weyl groups, is related to the character theory of the fixed subgroup of the diagram automorphism.
MSC:
20G Linear algebraic groups and related topics
Software:
GAP
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Digne, F., Shintani descent and L-functions on Deligne Lusztig varieties, Proc. Symp. Pure Math., 47, part 1, 61-68 (1987) · Zbl 0657.20036
[2] Fulton, W.; Harris, J., Representation theory, a first course, (Readings in Mathematics. Readings in Mathematics, Graduate Texts in Mathematics, vol. 129 (1991), Springer-Verlag: Springer-Verlag New York) · Zbl 0744.22001
[3] GAP - groups, algorithms, and programming, version 4.10.2 (2019)
[4] Kawanaka, N., Liftings of irreducible characters of finite classical groups. I, J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math., 28, 3, 851-861 (1981), (1982) · Zbl 0499.20027
[5] Kumar, S.; Lusztig, G.; Prasad, D., Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups, (Representation Theory. Representation Theory, Contemporary Math., vol. 478 (2009), AMS), 99-101 · Zbl 1160.20037
[6] Littlewood, D. E., The Theory of Group Characters and Matrix Representations of Groups (1940), Oxford University Press: Oxford University Press New York · JFM 66.0093.02
[7] Littlewood, D. E., Modular representations of symmetric groups, Proc. R. Soc. Lond. Ser. A, 209, 333-353 (1951) · Zbl 0044.25702
[8] Lusztig, G., Left cells in Weyl groups. Lie group representations, I, (College Park, Md., 1982/1983. College Park, Md., 1982/1983, Lecture Notes in Math., vol. 1024 (1983), Springer: Springer Berlin), 99-111
[9] Prasad, D., A character relationship on \(\operatorname{GL}_n(\mathbb{C})\), Isr. J., 211, 257-270 (2016)
[10] Robinson, G. de B., Representation Theory of the Symmetric Group, Mathematical Expositions, vol. 12 (1961), University of Toronto Press: University of Toronto Press Toronto, vii+204 pp · Zbl 0102.02002
[11] Shintani, T., Two remarks on irreducible characters of finite general linear groups, J. Math. Soc. Jpn., 28, 2, 396-414 (1976) · Zbl 0323.20041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.