We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes O1, O2 of G, with O1 spherical, lie in the same birational sheet, up to a shift by a central element of G, if and only if the coordinate rings of O1 and O2 are isomorphic as G-modules. As a consequence, we prove a conjecture of Losev for the spherical subvariety of the Lie algebra of G.
Spherical birational sheets in reductive groups
Ambrosio Filippo
;Costantini Mauro
2021
Abstract
We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes O1, O2 of G, with O1 spherical, lie in the same birational sheet, up to a shift by a central element of G, if and only if the coordinate rings of O1 and O2 are isomorphic as G-modules. As a consequence, we prove a conjecture of Losev for the spherical subvariety of the Lie algebra of G.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
spherical_bir.pdf
accesso aperto
Tipologia:
Postprint (accepted version)
Licenza:
Creative commons
Dimensione
637.27 kB
Formato
Adobe PDF
|
637.27 kB | Adobe PDF | Visualizza/Apri |
Birational_JA.pdf
solo utenti autorizzati
Tipologia:
Published (publisher's version)
Licenza:
Accesso privato - non pubblico
Dimensione
633.23 kB
Formato
Adobe PDF
|
633.23 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.