This article is cited in 1 paper

Recursive properties of branching and BGG resolution

V. D. Lyakhovsky, A. A. Nazarov

St. Petersburg State University, St. Petersburg, Russia

Abstract: 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.

Received: 19.11.2011

DOI: 10.4213/tmf6723

 English version: Theoretical and Mathematical Physics, 2011, 169:2, 1551–1560

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