Geodesic
Family Algebras and Generalized Exponents for Polyvector Representations of Simple Lie Algebras of Type~$B_n$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 72-82

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We give an explicit formula for the exterior powers $\wedge^k\pi_1$ of the defining representation $\pi_1$ of the simple Lie algebra $\mathfrak{so}(2n+1,\mathbb{C})$. We use the technique of family algebras. All representations in question are children of the spinor representation $\sigma$ of $\mathfrak{so}(2n+1,\mathbb{C})$. We also give a survey of main results on family algebras.
Keywords: family algebra, generalized exponent, representation of Lie algebra, spinor representation. 
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     author = {A. A. Kirillov},
     title = {Family {Algebras} and {Generalized} {Exponents} for {Polyvector} {Representations} of {Simple} {Lie} {Algebras} of {Type~}$B_n$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {72--82},
     publisher = {mathdoc},
     volume = {42},
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     year = {2008},
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A. A. Kirillov. Family Algebras and Generalized Exponents for Polyvector Representations of Simple Lie Algebras of Type~$B_n$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 72-82. http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a5/