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A Method for Weight Multiplicity Computation Based on Berezin Quantization
Let be a compact semisimple Lie group and be a maximal torus of .
We describe a method for weight multiplicity computation in unitary irreducible
representations of , based on the theory of Berezin quantization on .
Let be the reproducing kernel Hilbert
space of holomorphic sections of the homogeneous line bundle
over associated with the highest weight
of the irreducible representation of . The multiplicity of a
weight in is computed from functional analytical structure
of the Berezin symbol of the projector in onto subspace of weight . We describe a method
of the construction of this symbol and the evaluation of the weight
multiplicity as a rank of a Hermitian form. The application of this method is
described in a number of examples
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