Global bases for Bosonic extensions of quantum unipotent coordinate rings

Key Points

• The research establishes a global basis theory for bosonic extensions associated with Cartan matrices, enhancing quantum algebra understanding.
• It finds that for simply laced finite types, the bosonic extension relates to the quantum Grothendieck ring of the associated category.
• The study shows a correspondence between characters of simple modules and the normalized global basis, providing deeper insights into module theory.
• This advances the field by linking classical algebra concepts to quantum affine structures, suggesting potential applications in mathematical physics.