Abstract
We investigate a novel symmetry in dualities of Wu's equation: wg(1+w)1-g=eβ(ε-μ) for a degenerate g-on gas with fractional exclusion statistics of g, where β=1/k B T, ∊ the energy, and μ the chemical potential of the system. We find that the particle–hole duality between g and 1/g and the supersymmetric duality between g and 1-g form a novel quasi-modular group of order six for Wu's equation. And we show that many physical quantities in quantum systems with the fractional exclusion statistics can be represented in terms of quasi-hypergeometric functions and that the quasi-modular symmetry acts on these functions.
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