TY - JOUR
T1 - On the structure of parabolic subgroups
AU - Anchouche, Boudjemaa
PY - 2005
Y1 - 2005
N2 - Let G be a compact connected semisimple Lie group, Gℂ its complexification and let P be a parabolic subgroup of GC. Let P = L.Ru(P) be the Levi decomposition of P, where L is the Levi component of P and Ru(P) is the unipotent part of P. The group L acts by the adjoint representation on the successive quotients of the central series u(p) = u(0)(p) ⊃ u(1)(p) ⊃ . . . ⊃ u(i)(p) ⊃ . . . ⊃ u(r-1)(p) ⊃ u(r)(p) = 0, where u(p) is the Lie algebra of Ru(P). We determine for each 0 ≤ i ≤ r - 1 the irreducible components Vi(n1, ..., nv) of the adjoint action of L on u(i)(p)/u(i+1)(p).
AB - Let G be a compact connected semisimple Lie group, Gℂ its complexification and let P be a parabolic subgroup of GC. Let P = L.Ru(P) be the Levi decomposition of P, where L is the Levi component of P and Ru(P) is the unipotent part of P. The group L acts by the adjoint representation on the successive quotients of the central series u(p) = u(0)(p) ⊃ u(1)(p) ⊃ . . . ⊃ u(i)(p) ⊃ . . . ⊃ u(r-1)(p) ⊃ u(r)(p) = 0, where u(p) is the Lie algebra of Ru(P). We determine for each 0 ≤ i ≤ r - 1 the irreducible components Vi(n1, ..., nv) of the adjoint action of L on u(i)(p)/u(i+1)(p).
KW - Central series
KW - Irreducible representations
KW - Parabolic subgroups
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U2 - 10.36045/bbms/1133793339
DO - 10.36045/bbms/1133793339
M3 - Article
AN - SCOPUS:33744970921
SN - 1370-1444
VL - 12
SP - 521
EP - 524
JO - Bulletin of the Belgian Mathematical Society - Simon Stevin
JF - Bulletin of the Belgian Mathematical Society - Simon Stevin
IS - 4
ER -