| Wed, Apr 25, 2018
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Lie Groups Seminar
4:00 PM
MSCS 509 | | Mars-Springer slices for U(p,q)
Ben Wyser, OSU
| | | Abstract: The orbits of $GL(p) \times GL(q)$ on the flag variety $GL(p+q)/B$ are parametrized by combinatorial gadgets called ``clans.'' There are notions of pattern inclusion and avoidance for clans, and there are some limited results which characterize certain properties of the orbit closures (for example, smoothness) by pattern avoidance criteria. But in fact, not all local properties can be characterized in this way. In a recent paper, coauthors Alex Woo and Alex Yong and I showed that a combinatorial generalization of pattern avoidance, called ``interval pattern avoidance,'' is in fact sufficient to characterize a very general class of local properties. This is really a geometric result, as it follows from an isomorphism of certain ``slices'' of the orbit closures in the event of an interval pattern embedding. In this talk, I will give some details regarding exactly what these slices look like and how the isomorphism works, illustrating with running examples. Time permitting, I will then say a bit on exactly what the interval pattern avoidance theorem tells us, as well as what it does not tell us. |
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