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list of common Mackey functors -- a list of common Cp-Mackey functors

Here we include a table of common Mackey functors for the group $C_p$. The Lewis diagrams have to be formatted in \substack in order to compile, apologies for their appearance.

Ravenel symbol Lewis diagram Description Implementation
$\square$ $$\substack{\ZZ \\ p\uparrow\downarrow 1\\ \ZZ \\ \circlearrowleft \\ 1}$$ fixed point Mackey functor of $\ZZ$ as a trivial $C_p$-module makeFixedPointMackeyFunctor(p,id_(ZZ^1))
$\circ$ $$\substack{\ZZ/p \\ 0\uparrow\downarrow 0\\ 0 \\ \circlearrowleft \\ 1}$$ the zero-on-bottom Mackey functor associated to $\ZZ/p$ makeZeroOnUnderlyingMackeyFunctor(p,coker(matrix{{p}}))
$$\substack{\ZZ \\ 1\uparrow\downarrow p\\ \ZZ \\ \circlearrowleft \\ 1}$$ the orbit Mackey functor of $\Z$ makeOrbitMackeyFunctor(p,id_(ZZ^1))
$\ominus^n$ $$\substack{\ZZ / (q^n-1) \\ 1\uparrow\downarrow \sum_{j=0}^{p-1} q^{nj} \\ \ZZ/ (q^{np} - 1) \\ \circlearrowleft \\ q^n}$$ the fixed point Mackey functor of the algebraic $K$-group $K_{2n-1}(\mathbb{F}_{q^p})$ for a prime power $q$ makeKGroupMackeyFunctor(p,q,n)

The source of this document is in CpMackeyFunctors/Documentation/ListOfCommonMFsDoc.m2:17:0.