q-Deformed character theory for infinite-dimensional symplectic and orthogonal groups

Creators: Cuenca, Cesar; Gorin, Vadim

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.

Additional Information

© 2020 Springer Verlag. Published 12 June 2020. We would like to thank G. Olshanski for encouraging us to study whether the extension of [15] to orthogonal and symplectic groups is possible and for a number of fruitful discussions. V.G. was partially supported by the NSF Grant DMS-1664619, NSF Grant DMS-1949820, by the NEC Corporation Fund for Research in Computers and Communications, and by the Sloan Research Fellowship. The authors also thank the organizers of the Park City Mathematics Institute research program on Random Matrix Theory, where part of this work was carried out.

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