Abstract
We define and study cocycles on a Coxeter group in each degree generalizing the sign function. When the Coxeter group is a Weyl group, we explain how the degree three cocycle arises naturally from geometric representation theory.
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Private communication.
References
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Acknowledgements
The author would like to thank G. Lusztig for the collaboration on [3] from which the cocycle \(\epsilon _{3}^{W}\) was discovered, and for his helpful comments on the draft. He also thanks R. Bezrukavnikov, P. Etingof and D. Nadler for stimulating discussions. He thanks the referees for helpful suggestions.
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Partially supported by the Packard Foundation.
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Yun, Z. Higher Signs for Coxeter Groups. Peking Math J 4, 285–303 (2021). https://doi.org/10.1007/s42543-020-00029-z
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DOI: https://doi.org/10.1007/s42543-020-00029-z