complexLinearizationMap -- returns the complex linearization map for the prime p

Usage:

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

Description

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

i1 : complexLinearizationMap(5)

o1 =         fix : | 1 1 |
                   | 0 1 |
                   | 0 1 |
                   | 0 1 |
                   | 0 1 |
       5  <-----------------   2
     ZZ                      ZZ
     ^ |                     ^ | 
     | |                     | | 
     | v                     | v 
       1  <-----------------   1
     ZZ      und : | 1 |     ZZ
     ^ |                     ^ | 
     └-┘                     └-┘ 

o1 : MackeyFunctorHomomorphism

Ways to use complexLinearizationMap:

complexLinearizationMap(ZZ)

For the programmer

The object complexLinearizationMap 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.m2:207:0.

complexLinearizationMap -- returns the complex linearization map for the prime p

Description

See also

Ways to use complexLinearizationMap:

For the programmer