Timeline for Interaction of plethysm with other operations

7 events

when toggle format	what		by	license	comment
Sep 1, 2020 at 2:00	history	became hot network question
Aug 31, 2020 at 19:47	vote	accept	eti902
Aug 31, 2020 at 19:39	answer	added	Mark Wildon		timeline score: 6
Aug 31, 2020 at 19:16	comment	added	darij grinberg		The same applies to $f\left[uv\right]$, but this time you need the second comultiplication (i.e., the internal comultiplication, whose structure constants are the Kronecker coefficients) instead of $\Delta$.
Aug 31, 2020 at 19:16	comment	added	darij grinberg		If a symmetric function $f$ satisfies $\Delta\left(f\right) = \sum_{i=1}^k g_i \otimes h_i$ (where $\Delta$ is the comultiplication of the Hopf algebra of symmetric functions), then $f\left[u + v\right] = \sum_{i=1}^k g_i\left[u\right] h_i\left[v\right]$ whenever $u$ and $v$ are elements of a $\lambda$-ring (e.g., symmetric functions). Thus, any formula for $\Delta s_\nu$ (for example, the classical $\Delta s_\nu = \sum_{\lambda, \mu} c^\nu_{\lambda, \mu} s_\lambda \otimes s_\mu$) will give you a formula for $s_\nu\left[u + v\right]$.
Aug 31, 2020 at 18:01	history	edited	eti902		Change tags
Aug 31, 2020 at 17:54	history	asked	eti902	CC BY-SA 4.0