Diagonal orbits in double flag varieties

Abstract:

Given a parabolic subgroup $W_I$ of a Coxeter system $(W,S)$, the set of left cosets $w{W}_I$, 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