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arXiv · 1812.06523

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

Cesar Cuenca·Vadim Gorin
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Abstract

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.

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Cesar Cuenca, Vadim Gorin. 2018-12-16. q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups. https://arxiv.org/abs/1812.06523

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