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Let $\mathtt{k}$ be an algebraically closed field of characteristic zero. Let${\stackrel{{\rm o}}{{\mathfrak{g}}}}$ be the Lie superalgebra${\mathfrak{sl}}(n|m)$ and let $\mathfrak{W}$ be the Weyl groupoid introducedby  Sergeev and Veselov using the root system of ${\stackrel{{\rmo}}{{\mathfrak{g}}}}$. An important subgroupoid $\mathfrak T_{iso}$ of${\mathfrak{W}}$ has base $\Delta_{iso}$, the set of all the isotropic roots.  Motivated by deformed quantum Calogero-Moser problems, the same authorsconsidered an action of $\mathfrak{W}$ on $\mathtt{k}^{n|m}$ depending on aparameter $\kappa$. %When $\kappa$ is negative special, they showed this actionhas infinite orbits. In the case $m>n$, with $m,n $ relatively prime and$\kappa=-n/m$ we study a particular infinite orbit of $\mathfrak T_{iso}$ withsome special properties. This orbit, thought of as a directed graph isisomorphic to the graph of an orbit for the action of $\mathfrak T_{iso}$ oncertain Borel subalgebras of the affinization ${\widehat{L}(\stackrel{{\rm_o}}{{\mathfrak{g}}})}$ of ${\stackrel{{\rm o}}{{\mathfrak{g}}}}$. %The rootgroupoid has a base consisting of Borel subalgebras with fixed even part, andmorphisms are given by odd reflections.  The underlying reason for this graph isomorphism is that both havecombinatorics which can be described using Young diagrams and tableaux drawn onthe surface of a rotating cylinder with circumference $n$ and length $m$.Allowing the cylinder to rotate produces an infinite orbit. This leads to athird graph which is isomorphic to the other two.

The Weyl groupoid in Type A, Young diagrams and Borel subalgebras