| Wed, Sep 20, 2017
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Lie Groups Seminar
4:30 PM
MSCS 509 | | Nilpotent Orbits and Group Actions on the Flag Variety (A Combinatorial Approach), Part A
Leticia Barchini and Nina Williams, A Duet, OSU
| | | Abstract: We consider the pair of complex Lie groups $$(G, K) =\left(GL(p+q, \mathbb C), GL(p,\mathbb C)\times GL(q,\mathbb C)\right)$$
and the finite set $\{ \EuScript Q :\text{$K$-orbits on the flag variety } \mathfrak B \}$.
The moment map, $\mu$, of the $G$-action on the cotangent
bundle $T^*\mathfrak B$ maps each conormal bundle closure $\bar{T^*_{\EuScript Q} \mathfrak B}$ onto the closure of a single nilpotent
$K$-orbit, $\mathcal O_K$. We use combinatorial techniques to describe $\mu^{-1}(\mathcal O_K) = \{\EuScript Q \in \mathfrak B : \mu(T_\EuScript Q^*\mathfrak B) = \mathcal O_K \}$. |
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