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LieAlgebras: Add Demazure character #4339

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Implemented by the request of @lgoettgens and @gfourier
I am still writing documentation and tests

@lgoettgens lgoettgens added topic: LieAlgebras experimental Only changes experimental parts of the code labels Nov 21, 2024
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Just for future reference: @janikapeters is a student assistant at RWTH Aachen under the supervision of @gfourier and me working on project A24, in particular in extending the BasisLieHighestWeight experimental project to work for Demazure modules.

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function demazure_character(R::RootSystem, hw::Vector{<:IntegerUnion}, x::WeylGroupElem)
return demazure_character(WeightLatticeElem(R, hw), x)
end
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please also add dispatches that take a LieAlgebra as the first argument (cf. the character methods in LieAlgebraModule.jl), and ones that take a word instead of a WeylGroupElem.

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codecov bot commented Nov 21, 2024

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.51%. Comparing base (aea00d0) to head (eafc842).
Report is 51 commits behind head on master.

Additional details and impacted files
@@            Coverage Diff             @@
##           master    #4339      +/-   ##
==========================================
+ Coverage   84.48%   84.51%   +0.02%     
==========================================
  Files         641      645       +4     
  Lines       85427    85679     +252     
==========================================
+ Hits        72170    72408     +238     
- Misses      13257    13271      +14     
Files with missing lines Coverage Δ
experimental/LieAlgebras/src/LieAlgebras.jl 100.00% <ø> (ø)
experimental/LieAlgebras/src/RootSystem.jl 92.44% <100.00%> (-0.04%) ⬇️
...rimental/LieAlgebras/test/LieAlgebraModule-test.jl 100.00% <100.00%> (ø)

... and 75 files with indirect coverage changes

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