(Ir)Reducibility of some commuting varieties associated with involutions

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Here we prove that a commuting variety associated with a symmetric pair (g, g_0) is irreducible for (so_{n+m}, so_n + so_m) and reducible for (gl_{n+m}, {gl}_n + gl_m) with n>m, (so_{2n}, gl_n) with odd n, (E_6, {so}_{10} + k).
New examples of reducible commuting varieties are added

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Representation Theory, Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/74825

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504145
 http://arxiv.org/abs/math/0504145

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arXiv