On the inducing of unipotent classes for semisimple algebraic groups. I: Case of exceptional type
Let \(G\) be a connected semisimple algebraic group over an algebraically closed field \(K\). Let \(P\) be a parabolic subgroup of \(G\), \(L\) a Levi subgroup and \(U_ P\) the unipotent radical of \(P\). For a conjugate class \(C\) of unipotent elements in \(L\), the induced class \(C'=\mathrm{Ind}^ G_{L,P}C\) is defined as the unique class in \(G\) which intersects \(CU_ P\) densely [cf. \textit{G. Lusztig} and \textit{N. Spaltenstein}, J. Lond. Math. Soc., II. Ser. 19, 41--52 (1979; Zbl 0407.20035)]. Assuming that the characteristic of \(K\) is zero, the author studies how one can determine \(C'\) from \(C\) explicitly, when \(G\) is of exceptional type.
scientific article; zbMATH DE number 3857368