Journal of Lie Theory 35 (2025), No. 1, 037--054
Copyright Heldermann Verlag 2025
Biregular Elements in Radicals of Parabolic Subgroups in GL(n)
Aleksandr N. Panov
Mechanical and Mathematical Faculty, National Research University, Samara, Russia
apanov@list.ru
A biregular element in the radical u of the parabolic subgroup P is an element that is regular with respect to the adjoint actions of P and its maximal unipotent subgroup N simultaneously. We present a canonical biregular element in the radical of the parabolic subgroup of GL(n). We construct a system of free generators of the field of AdN-invariants K(u)N.
Keywords: Theory of invariants, parabolic subgroups, unipotent subgroup, adjoint orbits, nilpotent matrix.
MSC: 17B45, 20G07, 13A50.
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