Lusztig Induction, Unipotent Supports, and Character Bounds
| Autor: | Taylor, Jay, Tiep, Pham H. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. 373 (2020), no. 12, 8637--8676 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/8188 |
| Popis: | Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in a $(\mathbf{G},F)$-split Levi subgroup $\mathbf{M}$ of $\mathbf{G}$ and that $\mathbf{G}$ is defined over a field of good characteristic. In this paper, assuming a weak version of Lusztig's conjecture relating irreducible characters and characteristic functions of character sheaves holds, we considerably generalize this result by removing the condition that $\mathbf{M}$ is split. This assumption is known to hold whenever $Z(\mathbf{G})$ is connected or when $\mathbf{G}$ is a special linear or symplectic group and $\mathbf{G}$ is defined over a sufficiently large finite field. Comment: 35 pages; v2. minor improvements to abstract and introduction; v3. further improvements to the exposition; v4. significant changes. Main result now works for special linear and symplectic groups. Added results on groups of type A generalising results of Hildebrand; v5. post referee report |
| Databáze: | arXiv |
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