Geodesic
Products of Young symmetrizers and ideals in the generic tensor algebra
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 2, pp. 247-270.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We describe a formula for computing the product of the Young symmetrizer of a Young tableau with the Young symmetrizer of a subtableau, generalizing the classical quasi-idempotence of Young symmetrizers. We derive some consequences to the structure of ideals in the generic tensor algebra and its partial symmetrizations. Instances of these generic algebras appear in the work of S. Sam and A. Snowden ["Introduction to twisted commutative algebras", Preprint, arXiv:1209.5122] on twisted commutative algebras, as well as in the work of the author on the defining ideals of secant varieties of Segre-Veronese varieties, and in joint work of L. Oeding and the author ["Tangential varieties of Segre-Veronese varieties", Preprint, arXiv:1111.6202] on the defining ideals of tangential varieties of Segre-Veronese varieties.
Classification : 05E10, 05E15
Keywords: Young symmetrizers, Young tableaux, generic tensor algebra 
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     author = {Raicu, Claudiu},
     title = {Products of {Young} symmetrizers and ideals in the generic tensor algebra},
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Raicu, Claudiu. Products of Young symmetrizers and ideals in the generic tensor algebra. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 2, pp. 247-270. http://geodesic.mathdoc.fr/item/JAC_2014__39_2_a8/