Abstract
In a few mysterious lines of QSA VI Alfred Young introduced the notion of Raising operator. Very sketchily he goes through some rather remarkable manipulations to derive what is now sometimes referred to as Young's rule. In previous joint work [3] we have made rigorous a portion of Young's argument by interpreting these operators as acting on Ferrers' diagrams. Other authors, somewhat later have presented similar interpretations (see [8] and [10]). In the present work we bring some evidence to suggest that in Young's interpretation, raising operators acted on Tableaux rather than shapes. With this view, we can finally put together a rigorous version of the remaining unexplained portion of Young's treatment. This effort has also led us to a remarkably elementary and very combinatorial proof of Pieri's rule.
Work supported by NSF grant at the Univ. of Cal. San Diego and by ONR grant at the MIT.
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© 1986 Springer-Verlag
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Garsia, A.M. (1986). Raising operators and Young's rule. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072511
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DOI: https://doi.org/10.1007/BFb0072511
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