Abstract
We continue our study of the inclusion posets of diagonal SL(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 SL(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.
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Acknowledgments
The first author is partially supported by a grant from Louisiana Board of Regents. The authors are grateful to John Stembridge for his publicly available software codes which were used in the computations of this paper. The authors thank the referees for their very helpful comments and suggestions.
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Can, M.B., Le, T. Diagonal Orbits in a Type A Double Flag Variety of Complexity One. Order 38, 97–110 (2021). https://doi.org/10.1007/s11083-020-09530-7
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DOI: https://doi.org/10.1007/s11083-020-09530-7