Weyl denominator formula

For a positive root system

Φ^{+}

,

\sum_{w \in W} (- 1)^{ℓ (w)} e^{wρ} = e^{ρ} \prod_{α \in Φ^{+}} (1 - e^{- α}) .

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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 102 / 5 / b / Solution

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