Abstract
For type \({{\tilde B}_3}\), we show that Lusztig’s conjecture on the structure of the based ring of the two-sided cell corresponding to the unipotent class in Sp6(ℂ) with 3 equal Jordan blocks needs modification.
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Acknowledgements
The second author was supported by National Key R&D Program of China (Grant No. 2020YFA0712600) and National Natural Science Foundation of China (Grant No. 11688101). The authors thank Roman Bezrukavnikov for kindly communicating his notice that Lusztig’s conjecture describing the summand of J in terms of equivariant sheaves on the square of a finite set does not hold as stated for the two-sided cell corresponding to the unipotent class in Sp6(ℂ) with 3 equal Jordan blocks and for helpful discussions, and thank George Lusztig for helpful comments. Part of the work was done during the first author’s visit to the AMSS (Academy of Mathematics and Systems Science, Chinese Academy of Sciences). The first author is very grateful to the AMSS for hospitality and for financial supports. The authors deeply thank the referees for careful reading and very detailed comments which lead significant improvement of the article.
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Qiu, Y., Xi, N. The based rings of two-sided cells in an affine Weyl group of type \({{\tilde B}_3}\), I. Sci. China Math. 66, 221–236 (2023). https://doi.org/10.1007/s11425-021-1945-7
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DOI: https://doi.org/10.1007/s11425-021-1945-7