Timeline for Is a complete homogeneous symmetric polynomial irreducible?

6 events

when toggle format	what		by	license	comment
May 26, 2012 at 17:54	history	edited	Patricia Hersh	CC BY-SA 3.0	deleted 43 characters in body
May 26, 2012 at 17:39	comment	added	Patricia Hersh		It is well known in symmetric functions that $h_1,…,h_n$ are algebraically independent in ${\bf Q}[x_1,…,x_n]$ and that the symmetric functions $h_{\lambda }=h_{\lambda_1}⋯h_{\lambda_k}$ for $\lambda = (\lambda_1,\dots ,\lambda_k)$ with $\lambda_1\ge \lambda_2\ge \cdots \ge\lambda_k$ and $\sum \lambda_i = d$ form a vector space basis for the degree $d$ homogeneous piece of the ring of symmetric functions in $n$ variables. Hence my claim about needing nonsymmetric factors if there were going to be a nontrivial factorization.
May 26, 2012 at 16:49	history	edited	Patricia Hersh	CC BY-SA 3.0	deleted 287 characters in body; added 1 characters in body
May 26, 2012 at 16:22	history	edited	Patricia Hersh	CC BY-SA 3.0	added 38 characters in body
May 26, 2012 at 16:16	history	edited	Patricia Hersh	CC BY-SA 3.0	added 788 characters in body; added 38 characters in body; added 1 characters in body
May 26, 2012 at 15:19	history	answered	Patricia Hersh	CC BY-SA 3.0