3 problems

Let $\mu$ be a probability measure and let $[\mu]_\tau$ denote its free compression for $\tau\in[0,1]$. Define the sub-probability measure $\mu_\tau$ of total mass $\tau$ by…

Fix partitions ${\lambda}/{\mu}$ and ${\nu}$. Let $\psi_k:GT_{k{\lambda}/k{\mu},k{\nu}}\to GT_{{\lambda}/{\mu},{\nu}}$ be the map sending a pattern to the unique lexicographically…

Fix partitions ${\lambda}/{\mu}$ and ${\nu}$, let $G$ be an element of $GT_{{\lambda}/{\mu},{\nu}}$, and define … Here $GT_{{\lambda}/{\mu},{\nu}}$ denotes the set of Gelfand–Tsetl…