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The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
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Restriction of characters of hyperoctahedral groups.
Even though you found the answer, I'd like to point to the following reference, where I learned this result, at a time when the book by Macdonald (note the captitalization) did not yet have an appendi …
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Has Reifegerste's Theorem on RSK and Knuth relations received a slick proof by now?
First, just for clarity about the question, the Reifegerste preprint dates from September 2003, her paper was published in 2004, and Jacob Post's thesis is from 2009.
But the theorem is easy to show f …