Document Type

Honors Project On-Campus Access Only


The object of our study is a bijective algorithm that turns a word in the k-dimensional positive integer lattice into a sequence of standard Young tableaux, where the subsequence of every other tableaux, beginning with the first entry in said sequence, is a sequence of standard Young tableaux on n boxes, and each successive tableau is gotten by deleting a box and reinserting it. The tableaux in these subsequences index bases of irreducible modules for the symmetric group of degree n, and this bijection gives a combinatorial model for the decomposition of the k-th tensor power of the symmetric group permutation module into irreducibles. The algorithm embeds the crystal graphs of these irreducible modules into k-dimensional Euclidean space at the point corresponding to its given word, and we explore connections between the algebra and the geometry of this embedding.



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