Abstract
This article gives an explicit description of refined Bruhat cells. This description allows for an analysis of their closure patterns as well as for the calculation of structure constants of the endomorphism algebra of Gelfand–Graev representations. Most of the results rely on ideas and methods developed by V. Deodhar and C. Curtis.
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Acknowledgments
I would like to thank Prof. C. Curtis and Prof. D. Testerman for helpful remarks on different aspects of the manuscript. I also acknowledge the support of the Swiss National Science Foundation (Project Number P2ELP2_148913) and thank Prof. G. Malle for hosting me at TU Kaiserslautern. I am grateful for the remarks of the referees which improved the initial manuscript.
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Simion, I.I. On refinements of the Bruhat decomposition. J Algebr Comb 43, 75–100 (2016). https://doi.org/10.1007/s10801-015-0626-x
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DOI: https://doi.org/10.1007/s10801-015-0626-x