Mirkovic-Vilonen polytopes lying in a Demazure crystal and an opposite Demazure crystal

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dc.creatorNaito, Satoshi
dc.creatorSagaki, Daisuke
dc.date2008-06-19
dc.date2008-10-24
dc.date.accessioned2026-07-07T10:12:35Z
dc.date.available2026-07-07T10:12:35Z
dc.descriptionWe give a necessary and sufficient condition for an MV polytope $P$ in a highest weight crystal to lie in an arbitrary fixed Demazure crystal (resp., opposite Demazure crystal), in terms of the lengths of edges along a path through the 1-skeleton of $P$ corresponding to a reduced word for the longest element of the Weyl group $W$. % Also, we give an explicit description as a pseudo-Weyl polytope for extremal MV polytopes in a highest weight crystal. % Finally, by combining the results above, we obtain a polytopal condition for an MV polytope $P$ to lie in an arbitrary fixed opposite Demazure crystal.
dc.identifierhttps://arxiv.org/abs/0806.3112
dc.identifierhttp://arxiv.org/abs/0806.3112
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172230
dc.subjectQuantum Algebra
dc.titleMirkovic-Vilonen polytopes lying in a Demazure crystal and an opposite Demazure crystal
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