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University of Birmingham > Talks@bham > Algebra seminar > Minimum eigenspace codimension in irreducible representations of simple classical linear algebraic groups
![]() Minimum eigenspace codimension in irreducible representations of simple classical linear algebraic groupsAdd to your list(s) Download to your calendar using vCal
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 Vg(μ) denote the eigenspace corresponding to the eigenvalue μ ∈ k∗ of g ∈ G on V and define νG(V)=min{dim(V) − dim(Vg(μ)) | g ∈ G \ Z(G), μ ∈ k∗} to be the minimum eigenspace codimension on V. In this talk, we determine νG(V) for G of type Al, l ≥ 16 and dim(V) ≤l3/2; for G of type Bl, Cl, l ≥ 14 and dim(V) ≤ 4l3; and for G of type Dl, 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 νG(V). This talk is part of the Algebra seminar series. This talk is included in these lists:Note that ex-directory lists are not shown. |
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