Computing tensor product decompositions

ABSTRACT

An algorithm is presented for computing the decomposition of a tensor product of two irreducible representations of a semisimple complex Lie group into its irreducible components. The algorithm uses a known formula which expresses the multiplicities of the highest weight vectors in the decomposition as an alternating sum indexed by the Weyl group. This sum is accomplished with minimal memory requirements using techniques developed previously by the author for efficiently computing Weyl group orbits. Examples are given for each of the exceptional Lie groups.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

General Terms:
Algorithms, Experimentation, Measurement, Performance, Theory

Keywords:
algorithms measurement, performance, theory