An Asymptotic Result on the A-component in Iwasawa Decomposition
نویسنده
چکیده
Let G be a real connected semisimple Lie group. For each v′, v, g ∈ G, we prove that lim m→∞ [a(vgv)] = s · b(g), where a(g) denotes the a-component in the Iwasawa decomposition of g = kan and b(g) ∈ A+ denotes the unique element that conjugate to the hyperbolic component in the complete multiplicative Jordan decomposition of g = ehu. The element s in the Weyl group of (G, A) is determined by yv ∈ G (not unique in general) in such a way that yv ∈ NmsMAN , where yhy−1 = b(g) and G = ∪s∈WNmsMAN is the Bruhat decomposition of G.
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