COMBINATORIAL BASES FOR COVARIANT REPRESENTATIONS OF THE LIE SUPERALGEBRA glm|n
نویسنده
چکیده
Covariant tensor representations of glm|n occur as irreducible components of tensor powers of the natural (m + n)-dimensional representation. We construct a basis of each covariant representation and give explicit formulas for the action of the generators of glm|n in this basis. The basis has the property that the natural Lie subalgebras glm and gln act by the classical Gelfand–Tsetlin formulas. The main role in the construction is played by the fact that the subspace of glm-highest vectors in any finite-dimensional irreducible representation of glm|n carries a structure of an irreducible module over the Yangian Y(gln). One consequence is a new proof of the character formula for the covariant representations first found by Berele and Regev and by Sergeev.
منابع مشابه
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