q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups
Representation Theory
2018-12-18 v1 Combinatorics
Probability
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.
Keywords
Cite
@article{arxiv.1812.06523,
title = {q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups},
author = {Cesar Cuenca and Vadim Gorin},
journal= {arXiv preprint arXiv:1812.06523},
year = {2018}
}