Geodesic
Essential Signatures and Monomial Bases for Bn and Dn
Andrei A. Gornitskii1
1National Research University, Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow 111250, Russia
Journal of Lie Theory, Tome 29 (2019) no. 1, pp. 277-302

Voir la notice de l'article provenant de la source Heldermann Verlag

In the representation theory of simple Lie algebras, we consider the problem of constructing a monomial basis in an arbitrary irreducible finite-dimensional highest weight module. We construct a PBW-type basis in every finite-dimensional representation of Bn and Dn and we describe the associated semigroup of essential signatures. These bases are parameterized by integer points in some polytopes. We give the inequalities defining these polytopes.
Classification : 17B10, 17B20
Mots-clés : Simple Lie algebra, irreducible representation, weight basis, essential signature

Andrei A. Gornitskii  1

1 National Research University, Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow 111250, Russia 
Andrei A. Gornitskii. Essential Signatures and Monomial Bases for Bn and Dn. Journal of Lie Theory, Tome 29 (2019) no. 1, pp. 277-302. http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a13/
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     author = {Andrei A. Gornitskii},
     title = {Essential {Signatures} and {Monomial} {Bases} for {B\protect\textsubscript{n}} and {D\protect\textsubscript{n}}},
     journal = {Journal of Lie Theory},
     pages = {277--302},
     year = {2019},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a13/}
}
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