Blocks and Brauer trees for groups of type 𝐺₂(𝑞)

Shamash, Josephine

doi:10.1090/pspum/047.2/933418

Cited by 9 publications

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“…The irreducible character degrees and their multiplicities for 2 B 2 (q) and 3 D 4 (q) can be found in [47,5], and for G 2 (q) a summary can be found in [43,Appendix]. Inspection of this data shows that ζ G (s) → 1 for s > s 0 , where…”

Section: Corollary 24mentioning

confidence: 98%

Fuchsian groups, finite simple groups and representation varieties

Liebeck

Shalev

2005

Invent. math.

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Let Γ be a Fuchsian group of genus at least 2 (at least 3 if Γ is non-oriented). We study the spaces of homomorphisms from Γ to finite simple groups G, and derive a number of applications concerning random generation and representation varieties.Precise asymptotic estimates for |Hom(Γ, G)| are given, implying in particular that as the rank of G tends to infinity, this is of the form |G| μ(Γ)+1+o(1) , where μ(Γ) is the measure of Γ. We then prove that a randomly chosen homomorphism from Γ to G is surjective with probability tending to 1 as |G| → ∞. Combining our results with Lang-Weil estimates from algebraic geometry, we obtain the dimensions of the representation varieties Hom(Γ,Ḡ), whereḠ is GL n (K) or a simple algebraic group over K, an algebraically closed field of arbitrary characteristic.A key ingredient of our approach is character theory, involving the study of the 'zeta function' ζ G (s) = χ(1) −s , where the sum is over all irreducible complex characters χ of G.

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Section: Corollary 24mentioning

confidence: 98%

Fuchsian groups, finite simple groups and representation varieties

Liebeck

Shalev

2005

Invent. math.

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“…From the results about blocks and Brauer trees of G 2 (q) in [H1,HS1,HS2,S1,S2], we see that if 3 q then ψ = X 32 in all cases except when = 3 and q ≡ 1 (mod 3) where ψ = X 32 − 1 G . If 3 | q then ψ = X 22 except when = 2 where ψ = X 22 − 1 G .…”

Section: The Degrees Of Irreducible Brauer Characters Of G 2 (Q)mentioning

confidence: 89%

Irreducible restrictions of Brauer characters of the Chevalley group G2(q) to its proper subgroups

Nguyen

2008

Journal of Algebra

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“…In [92] Shamash has given the distribution of the irreducible characters X of G2(q) into r-blocks. It In the case of the general linear groups GL(n, q) Dipper and James have given another proof of Theorem 7.8 which is independent of the.…”

Section: Ref'mentioning

confidence: 99%

Contributions to Modular Representation Theory of Finite Groups

Michler¹

1991

Representation Theory of Finite Groups and Finite-Dimensional Algebras

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Blocks and Brauer trees for groups of type 𝐺₂(𝑞)

Cited by 9 publications

References 0 publications

Fuchsian groups, finite simple groups and representation varieties

Fuchsian groups, finite simple groups and representation varieties

Irreducible restrictions of Brauer characters of the Chevalley group G2(q) to its proper subgroups

Contributions to Modular Representation Theory of Finite Groups

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