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pro vyhledávání: '"Taylor, Jay"'
Let $\Gamma$ be a cocompact, oriented Fuchsian group which is not on an explicit finite list of possible exceptions and $q$ a sufficiently large prime power not divisible by the order of any non-trivial torsion element of $\Gamma$. Then $|\mathrm{Hom
Externí odkaz:
http://arxiv.org/abs/2407.07193
We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element is connected, then the map is Galois-equivariant. Further, in this situation, we show that ther
Externí odkaz:
http://arxiv.org/abs/2310.00237
For every integer $k$ there exists a bound $B=B(k)$ such that if the characteristic polynomial of $g\in \operatorname{SL}_n(q)$ is the product of $\le k$ pairwise distinct monic irreducible polynomials over $\mathbb{F}_q$, then every element $x$ of $
Externí odkaz:
http://arxiv.org/abs/2204.09262
Autor:
Taylor, Jay
Publikováno v:
Indag. Math. (N.S.) 33 (2022), no. 1, 24-38
The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that are labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those cuspidal pairs using results of Lusztig.
Externí odkaz:
http://arxiv.org/abs/2012.09674
Autor:
Fry, A. A. Schaeffer, Taylor, Jay
In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the first-name
Externí odkaz:
http://arxiv.org/abs/2005.14088
Publikováno v:
Ann. of Math. (2) 192 (2020), no. 2, 583--663
We show that the decomposition matrix of unipotent $\ell$-blocks of a finite reductive group $\mathbf{G}(\mathbb{F}_q)$ has a unitriangular shape, assuming $q$ is a power of a good prime and $\ell$ is very good for $\mathbf{G}$. This was conjectured
Externí odkaz:
http://arxiv.org/abs/1910.08830
Autor:
Taylor, Jay, Tiep, Pham H.
Publikováno v:
Trans. Amer. Math. Soc. 373 (2020), no. 12, 8637--8676
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 $(\math
Externí odkaz:
http://arxiv.org/abs/1809.00173
Autor:
Fry, A. A. Schaeffer, Taylor, Jay
Publikováno v:
Bull. Lond. Math. Soc., 50 (2018), 733-744
Let $G$ be a finite group with Sylow $2$-subgroup $P \leqslant G$. Navarro-Tiep-Vallejo have conjectured that the principal $2$-block of $N_G(P)$ contains exactly one irreducible Brauer character if and only if all odd-degree ordinary irreducible cha
Externí odkaz:
http://arxiv.org/abs/1710.08094