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On Quasi Steinberg Characters of Complex Reflection Groups

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Abstract

Let G be a finite group and p be a prime number dividing the order of G. An irreducible character χ of G is called a quasi p-Steinberg character if χ(g) is nonzero for every p-regular element g in G. In this paper, we classify the quasi p-Steinberg characters of complex reflection groups G(r,q,n) and exceptional complex reflection groups. In particular, we obtain this classification for Weyl groups of type Bn and type Dn.

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Acknowledgements

The authors are grateful to Dipendra Prasad for his encouragement regarding this project. The authors thank Anupam Singh and Manoj K. Yadav for organizing the Group Theory Sangam seminar series, during which one of the seminars led to this project. The authors would also like to thank the referee for their thorough reading and helpful suggestions, which significantly improved this article. The second named author acknowledges IISc Raman post doctoral fellowship for their support.

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Authors and Affiliations

  1. Faculdade de Matemática, Universidade Federal do Pará, Belém, Brazil

    Ashish Mishra

  2. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Digjoy Paul

  3. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Pooja Singla

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  1. Ashish Mishra
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  2. Digjoy Paul
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All the authors took active part in writing the main manuscript. All authors reviewed the manuscript.

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Correspondence to Ashish Mishra.

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Mishra, A., Paul, D. & Singla, P. On Quasi Steinberg Characters of Complex Reflection Groups. Algebr Represent Theor 26, 3101–3118 (2023). https://doi.org/10.1007/s10468-023-10201-5

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