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

Cesar Cuenca ^[1] ; Vadim Gorin ^[2]
1. [1] MIT; Caltech, USA
2. [2] MIT, USA; Institute for Information Transmission Problems,, Rusia; University of Wisconsin - Madison, USA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-00572-8
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Resumen
- 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.