Family algebras and generalized exponents for polyvector representations of simple Lie algebras of type B n
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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 wordsfamily algebra generalized exponent representation of Lie algebra spinor representation
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