Geodesic
Recursive properties of branching and BGG resolution
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 218-228

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Recurrence relations for branching coefficients are based on a certain decomposition of the singular element. We show that this decomposition can be used to construct parabolic Verma modules and to obtain the generalized Weyl–Verma formulas for characters. We also demonstrate that the branching coefficients determine the generalized Bernstein–Gelfand–Gelfand resolution.
Keywords: Lie algebra representation, branching rule, Bernstein–Gelfand–Gelfand resolution. 
@article{TMF_2011_169_2_a3,
     author = {V. D. Lyakhovsky and A. A. Nazarov},
     title = {Recursive properties of branching and {BGG} resolution},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {218--228},
     publisher = {mathdoc},
     volume = {169},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a3/}
}
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V. D. Lyakhovsky; A. A. Nazarov. Recursive properties of branching and BGG resolution. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 218-228. http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a3/