Generally, a Verlinde formula gives the dimension of a space of states of Chern-Simons theory for a given gauge group$G$. Depending on which one of various different algebraic means to expresses these spaces is used, the Verlinde formula equivalently computes the dimension of spaces of non-abelian theta functions, the dimension of objects in a modular tensor category and so forth.

There are also Verlinde formulas in algebraic geometry (proved by Faltings) and a related one in the theory of vertex operator algebras (proved only in very special cases).

References

Faltings

Mukai moduli space book

Dowker, On Verlindeâ€™s formula for the dimensions of vector bundles on moduli spaces, iopscience

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