The normalized Brézin-Gross-Witten numbers satisfy C(d) = 1/π + O(1/g(d)) uniformly in the number of marked points, with a polynomial structure in the large genus expansion.
Galilean symmetry of the KdV hierarchy
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By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish an explicit relationship between the non-abelian Born--Infeld partition function and the generalized Br\'ezin--Gross--Witten partition function.
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Combinatorics and large genus asymptotics of the Br\'ezin--Gross--Witten numbers
The normalized Brézin-Gross-Witten numbers satisfy C(d) = 1/π + O(1/g(d)) uniformly in the number of marked points, with a polynomial structure in the large genus expansion.