A weight basis of a Lie algebra representation is a basis consisting of weight vectors for a chosen Cartan subalgebra. When the Cartan action is diagonalizable, choose a basis separately in every weight space and combine them. This makes weight multiplicities directly visible and gives diagonal matrices for Cartan elements.

Ancestors (12)

  1. Weight-space decomposition
  2. Weight space
  3. Weight vector
  4. Highest-weight representation
  5. Semisimple Lie algebra
  6. Lie algebra
  7. Lie theory
  8. Diagonal dominance
  9. Algebra
  10. Area of mathematics
  11. Mathematics
  12. Home

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