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

## TL;DR

This paper extends the classification of irreducible spherical characters to q-deformed orthogonal and symplectic groups, providing new formulas and methods for understanding their asymptotic behavior.

## Contribution

It introduces a q-deformed character theory for infinite-dimensional orthogonal and symplectic groups, expanding previous results from the unitary case.

## Key findings

- Derived determinantal formulas for q-specialized characters
- Established double-contour integral representations
- Extended classification results to new group types

## 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.