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The classification of irreducible, spherical characters of theinfinite-dimensional unitary/orthogonal/symplectic groups can be obtained byfinding all possible limits of normalized, irreducible characters of thecorresponding finite-dimensional groups, as the rank tends to infinity. Wesolve a q-deformed version of the latter problem for orthogonal and symplecticgroups, extending previously known results for the unitary group. The proof isbased on novel determinantal and double-contour integral formulas for theq-specialized characters.

q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups