By specialization to the trace of the identity element, Weyl's character formula gives the Weyl dimension formula
for the dimension of a finite dimensional representation VΛ with highest weight Λ. (As usual, ρ is the Weyl vector and the products run over positive roots α.) The specialization is not completely trivial, because both the numerator and denominator of the Weyl character formula vanish to high order at the identity element, so it is necessary to take a limit of the trace of an element tending to the identity.
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