Minimum eigenspace codimension in irreducible representations of simple classical linear algebraic groups

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• Ana M. Retegan (University of Birmingham)
• Wednesday 09 November 2022, 15:00-16:00
• Lecture Theatre C, Watson Building.

If you have a question about this talk, please contact Matthew Westaway.

Let k be an algebraically closed field of characteristic p ≥ 0, let G be a simple simply connected classical linear algebraic group of rank l and let T be a maximal torus in G with rational character group X(T). For a non-zero p-restricted dominant weight λ ∈ X(T), let V be the associated irreducible kG-module. Let V_g(μ) denote the eigenspace corresponding to the eigenvalue μ ∈ k^∗ of g ∈ G on V and define

ν_G(V)=min{dim(V) − dim(V_g(μ)) | g ∈ G \ Z(G), μ ∈ k^∗}

to be the minimum eigenspace codimension on V. In this talk, we determine ν_G(V) for G of type A_l, l ≥ 16 and dim(V) ≤l³/2; for G of type B_l, C_l, l ≥ 14 and dim(V) ≤ 4l³; and for G of type D_l, l ≥ 16 and dim(V) ≤ 4l³. Moreover, for the groups of smaller rank and their corresponding irreducible modules with dimension satisfying the above bounds, we determine lower bounds for ν_G(V).

This talk is part of the Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• Lecture Theatre C, Watson Building
• School of Mathematics events

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