(Ir)Reducibility of some commuting varieties associated with involutions

Details (Ir)Reducibility of some commuting varieties associated with involutions (Ir)Reducibility of some commuting varieties associated with involutions

2005-04-07

arxiv.org/abs/math/0504145v2

Mathematics

Representation Theory

New examples of reducible commuting varieties are added

Scientific paper

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).

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