trivialRepresentation -- creates the trivial representation of a Lie algebra

Usage:

trivialRepresentation(LAB)
Inputs:
- LAB, an instance of the type LieAlgebraBasis,
Outputs:
- V, an instance of the type LieAlgebraRepresentation,

Description

The user may either input the Lie algebra basis, or the type and rank, or the simple Lie algebra.

i1 : rho0 = trivialRepresentation("A",2)

o1 = LieAlgebraRepresentation{"Basis" => Enhanced basis of 𝔞                      }
                                                            2
                              "Module" => LL   (𝔞 )
                                            0,0  2
                              "RepresentationMatrices" => {0, 0, 0, 0, 0, 0, 0, 0}

o1 : LieAlgebraRepresentation

i2 : V0 = rho0#"Module"

o2 = V0

o2 : irreducible LieAlgebraModule over 𝔞
                                        2

i3 : dim V0

o3 = 1

i4 : V0#"DecompositionIntoIrreducibles"

o4 = VirtualTally{{0, 0} => 1}

o4 : VirtualTally

Ways to use trivialRepresentation:

trivialRepresentation(LieAlgebra)
trivialRepresentation(LieAlgebraBasis)
trivialRepresentation(String,ZZ)

For the programmer

The object trivialRepresentation is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:1620:0.