The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding finite-dimensional groups, as the rank tends to infinity. We solve a q-deformed version of the latter problem for orthogonal and symplectic groups, extending previously known results for the unitary group. The proof is based on novel determinantal and double-contour integral formulas for the q-specialized characters.

中文翻译：

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q-无限维辛和正交群的变形特征理论

当秩趋于无穷大时，可以通过找到相应有限维组的归一化，不可约性字符的所有可能极限，来获得无限维unit合/正交/辛折点组的不可约球形字符的分类。我们为正交和辛群解决了后者问题的q变形形式，扩展了previously群的先前已知结果。该证明基于q特殊字符的新颖行列式和双轮廓积分公式。