Geodesic
Involutions in $S_n$ and associated coadjoint orbits
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 16, Tome 349 (2007), pp. 150-173

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In the paper we study the coadjoint orbits of the group $\mathrm{UT}(n,K)$ associated with involutions. We obtain a formula for dimension of the orbit. We construct a polarization for the canonical element of the orbit. We find a system of generators in the defining ideal of the orbit. 
@article{ZNSL_2007_349_a5,
     author = {A. N. Panov},
     title = {Involutions in $S_n$ and associated coadjoint orbits},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--173},
     publisher = {mathdoc},
     volume = {349},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a5/}
}
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A. N. Panov. Involutions in $S_n$ and associated coadjoint orbits. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 16, Tome 349 (2007), pp. 150-173. http://geodesic.mathdoc.fr/item/ZNSL_2007_349_a5/