Geodesic
Chow ring of horospherical varieties of Picard number one
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 147-163

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An algorithm based on Goresky–Kottwitz–MacPherson method is provided to compute the equivariant Chow ring of a horospherical variety of Picard number one. In the case of $G_2$-variety, an explicit presentation of this ring is given. 
@article{ZNSL_2022_513_a10,
     author = {V. A. Petrov and A. K. Sonina},
     title = {Chow ring of horospherical varieties of {Picard} number one},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--163},
     publisher = {mathdoc},
     volume = {513},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a10/}
}
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V. A. Petrov; A. K. Sonina. Chow ring of horospherical varieties of Picard number one. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 147-163. http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a10/