Abstract:
Given a parabolic subgroup \( W_I \) of a Coxeter system \( (W,S)\), the set of left cosets \( wW_I\), for \( I \subseteq S, w \in W\), is well-studied. However, the set of double cosets \( W_I w W_J \) for \( I,J \subseteq S\) is a less studied object. I want to analyze the double cosets, in particular, to investigate the conditions on \( I \) and \( J \) so that the set of double cosets carries some certain structure.
The main result that I have found is that: Let \$G\$ denote \$SL(n)\$ and let \$X\$ be a double flag variety \$G/P_1\times G/P_2\$. If \$c_G(X) \leq 1\$, then the inclusion poset of \$G\$-orbit closures in \$X\$ is a graded lattice.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974