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We continue our study of the inclusion posets of diagonal S L ( n )-orbit closures in a product of two partial flag varieties. We prove that, if the diagonal… Click to show full abstract
We continue our study of the inclusion posets of diagonal S L ( n )-orbit closures in a product of two partial flag varieties. We prove that, if the diagonal action is of complexity one, then the poset is isomorphic to one of the 28 posets that we determine explicitly. Furthermore, our computations show that the number of diagonal S L ( n )-orbits in any of these posets is at most 10 for any positive integer n . This is in contrast with the complexity 0 case, where, in some cases, the resulting posets attain arbitrary heights.
Keywords:
complexity;
diagonal orbits;
type double;
flag;
orbits type;
complexity one
Journal Title: Order
Year Published: 2021
Link to full text (if available)
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Journal Title: Order
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!