2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74825Here 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 addedRepresentation TheoryAlgebraic Geometrytext