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# realLinearizationMap -- returns the real linearization map for the prime p

- Usage:
    `realLinearizationMap(p)`
- Inputs:
  - p, an integer,
- Outputs:
  - a Mackey Functor homomorphism, the linearization map from the Burnside Mackey functor to the real representation functor for the prime p.

## Description

Every $G$-set $X$ determines a real representation with basis $X$, called the permutation representation of $X$. This induces a map from the Burnside Mackey functor to the real representation Mackey functor called the linearization map.

    i1 : realLinearizationMap(5)

    o1 =         fix : | 1 1 |
                       | 0 1 |
                       | 0 1 |
           3  <-----------------   2
         ZZ                      ZZ
         ^ |                     ^ |
         | |                     | |
         | v                     | v
           1  <-----------------   1
         ZZ      und : | 1 |     ZZ
         ^ |                     ^ |
         └-┘                     └-┘

    o1 : MackeyFunctorHomomorphism

## See also

- MackeyFunctorHomomorphism -- the class of Mackey functor homomorphisms
- complexLinearizationMap -- returns the complex linearization map for the prime p

## Ways to use realLinearizationMap:

- `realLinearizationMap(ZZ)`

## For the programmer

The object realLinearizationMap is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CpMackeyFunctors/Documentation/HomomorphismsDoc.m2:230:0.