Journal of Lie Theory

no. 1
Essential Signatures and Monomial Bases for Bn and Dn
Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 277-302
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.
DOI: 10.5802/jolt.1059
Classification: 17B10, 17B20
Keywords: Simple Lie algebra, irreducible representation, weight basis, essential signature 
@article{JOLT_2019_29_1_a13,
     author = {A. 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},
     doi = {10.5802/jolt.1059},
     zbl = {1433.17009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1059/}
}
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%J Journal of Lie Theory
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A. A. Gornitskii. Essential Signatures and Monomial Bases for Bn and Dn. Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 277-302. doi: 10.5802/jolt.1059

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