3 problems
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QP1–QP2 conjecture for conjugacy classes of twisted involutions
QP1–QP2 conjecture. Every conjugacy class in satisfying (QP1) also satisfies (QP2), and hence is quasiparabolic.
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Parabolic characterization conjecture for transitive quasiparabolic sets
Parabolic characterization conjecture. If
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Rains–Vazirani's bar-operator conjecture for quasiparabolic sets
Rains–Vazirani's bar-operator conjecture. If is bounded below, then each of the modules