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Essential signatures and canonical bases of irreducible representations of simple Lie algebras. (English. Russian original) Zbl 1433.17010

Russ. Math. Surv. 73, No. 5, 925-927 (2018); translation from Usp. Mat. Nauk 73, No. 5, 187-188 (2018).
From the text: In the present paper we consider the problem of constructing a canonical weight basis in the space of a finite-dimensional irreducible representation of a simple complex Lie algebra. We use the Vinberg method to construct such bases by applying lowering operators to the highest vector.

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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[1] T. Backhaus and D. Kus 2015 (v1 - 2015, v3 - 2016) The PBW filtration and convex polytopes in type B 1504.06522v2 31 pp.
[2] E. Feigin, G. Fourier, and P. Littelmann 2011 Transform. Groups16 1 71-89 · Zbl 1237.17011 · doi:10.1007/s00031-010-9115-4
[3] E. Feigin, G. Fourier, and P. Littelmann 2011 Int. Math. Res. Not. IMRN2011 24 5760-5784 · Zbl 1233.17007 · doi:10.1093/imrn/rnr014
[4] А. А. Горницкий 2015 Матем. заметки97 1 35-47 · doi:10.4213/mzm10384
[5] English transl. A. A. Gornitskii 2015 Math. Notes97 1 30-41 · Zbl 1377.17010 · doi:10.1134/S0001434615010046
[6] A. A. Gornitskii 2015 Essential signatures and canonical bases for irreducible representations of \(D_4\) 1507.07498 16 pp. · Zbl 1377.17010
[7] A. A. Gornitskii 2018 (v1 -2016) Essential signatures and canonical bases for \(B_n\) and \(D_n\) 1611.07381v2 33 pp.
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