ABCD of qq-characters
Satoshi Nawata (Department of Physics and Center for Field Theory and Particle Physics, Fudan University, 2005 Songhu Road, Shanghai, 200438, China); Kilar Zhang (Department of Physics, Shanghai University, 99 Shangda Road, Shanghai, 200444, China, Shanghai Key Lab for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai, 200234, China); Rui-Dong Zhu (Institute for Advanced Study & School of Physical Science and Technology, Soochow University, 333 Ganjiang Road, Suzhou, 215006, China)
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 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.
