ABCD of qq-characters

TL;DR

This paper derives explicit analytic expressions for qq-characters in 5d pure Yang-Mills theories with BCD gauge groups, revealing their algebraic structures and relationships among classical groups.

Contribution

It provides the first explicit formulas for qq-characters in BCD-type gauge groups using Young diagrams in the unrefined limit.

Findings

Explicit qq-character formulas for BCD gauge groups.

Construction of a quantum-toroidal-like algebra for SO(n).

Insights into relationships among classical gauge group qq-characters.

Abstract

The qq-characters are powerful tools to reveal symmetries and integrabilities of Seiberg-Witten theories. The goal of this paper is to provide analytic expressions of qq-characters based on Young diagrams in 5d $\mathcal{N} = 1$ pure Yang-Mills theories with BCD-type gauge groups, by focusing on the unrefined limit. Using these expressions, we investigate the relationships among qq-characters of classical gauge groups. For SO(n) gauge groups, we construct a quantum-toroidal-like algebra via the Ward-identity approach, which allows us to derive the qq-characters.