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On monomial linearisation and supercharacters of pattern subgroups

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Abstract

Column closed pattern subgroups U of the finite upper unitriangular groups U n (q) are defined as sets of matrices in U n (q) having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky's construction of monomial linearisation in his thesis and apply this to ℂU yielding a generalisation of Yan's coadjoint cluster representations. Then we give a complete classification of the resulting supercharacters, by describing the resulting orbits and determining the Hom-spaces between orbit modules.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11601338) and the German Research Foundation, Priority Programme Deutsche Forschungsgemeinschaft- Schwerpunktsprogramm Darstellungstheorie 1388 in Representation Theory (Grant No. 99028426). In addition, The authors thank the referees for interesting comments and valuable suggestions.

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Authors and Affiliations

  1. College of Sciences, Shanghai Institute of Technology, Shanghai, 201418, China

    Qiong Guo

  2. Institut für Algebra und Zahlentheorie, Universität Stuttgart, Stuttgart, 70569, Germany

    Richard Dipper

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  1. Qiong Guo
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  2. Richard Dipper
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Correspondence to Qiong Guo.

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Guo, Q., Dipper, R. On monomial linearisation and supercharacters of pattern subgroups. Sci. China Math. 61, 227–252 (2018). https://doi.org/10.1007/s11425-017-9213-x

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  • DOI: https://doi.org/10.1007/s11425-017-9213-x

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