A computational approach to the Frobenius–Schur indicators of finite exceptional groups

Trefethen, Stephen; Vinroot, C. Ryan

doi:10.1142/s0218196719500681

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…The main issue for general types is that the relationship between Frobenius-Schur indicators and the Lusztig-Jordan decomposition is not well-understood, cf. [TV20] for some results in this direction.…”

Section: Introductionmentioning

confidence: 96%

Character stacks are PORC count

Bridger¹,

Kamgarpour²

2022

Preprint

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We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key ingredients in the proof are Lusztig's Jordan decomposition of complex characters of finite reductive groups and Deriziotis's results on their genus numbers . As a consequence of our main theorem, we obtain an expression for the E-polynomial of the character stack.

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Section: Introductionmentioning

confidence: 96%

Character stacks are PORC count

Bridger¹,

Kamgarpour²

2022

Preprint

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“…A new interpretation of the F-S indicator in terms of superalgebras has been given recently in [13]. The case of the dihedral group D 8 shows that ǫ(χ) is not determined by the character table of G. The computation of F-S indicators can be a surprisingly difficult task, which has not been fully completed for the simple groups of Lie type, for instance (see [25]). Problem 14 on Brauer's famous list [2] asks for a group-theoretical interpretation of the number of χ ∈ Irr(G) with ǫ(χ) = 1.…”

Section: Introductionmentioning

confidence: 99%

Real characters in nilpotent blocks

Sambale¹

2023

Preprint

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We prove that the number of irreducible real characters in a nilpotent block of a finite group is locally determined. We further conjecture that the Frobenius-Schur indicators of those characters can be computed for p = 2 in terms of the extended defect group. We derive this from a more general conjecture on the Frobenius-Schur indicator of projective indecomposable characters of 2-blocks with one simple module. This extends results of Murray on 2-blocks with cyclic and dihedral defect groups.

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“…For , this is proved in [LRV20]. The main issue for general types is that the relationship between Frobenius–Schur indicators and the Lusztig–Jordan decomposition is not well understood; see [TV20] for some results in this direction.…”

Section: Introductionmentioning

confidence: 99%

Character Stacks Are Porc Count

BRIDGER¹,

Kamgarpour

2022

J. Aust. Math. Soc.

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We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a polynomial on residue classes (PORC). The key ingredients in the proof are Lusztig’s Jordan decomposition of complex characters of finite reductive groups and Deriziotis’s results on their genus numbers. As a consequence of our main theorem, we obtain an expression for the E-polynomial of the character stack.

show abstract

A computational approach to the Frobenius–Schur indicators of finite exceptional groups

Cited by 4 publications

References 38 publications

Character stacks are PORC count

Character stacks are PORC count

Real characters in nilpotent blocks

Character Stacks Are Porc Count

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