Functional Analysis and Its Applications

, Volume 42, Issue 4, pp 308–316 | Cite as

Family algebras and generalized exponents for polyvector representations of simple Lie algebras of type B n

  • A. A. Kirillov


We give an explicit formula for the exterior powers ∧ k π 1 of the defining representation π 1 of the simple Lie algebra ςο(2n + 1, ℂ). We use the technique of family algebras. All representations in question are children of the spinor representation σ of g2ο(2n + 1, ℂ). We also give a survey of main results on family algebras.

Key words

family algebra generalized exponent representation of Lie algebra spinor representation 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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