2025/03/31 by Morier-Genoud, Sophie, Ovsienko, Valentin · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2503.23834
The concept of q-deformation, or ``q-analogue'' arises in many areas of mathematics. In algebra and representation theory, it is the origin of quantum groups; q-deformations are important for knot invariants, combinatorial enumeration, discrete geometry, analysis, and many other parts of mathematics. In mathematical physics, q-deformations are often understood as ``quantizations''. The recently introduced notion of a q-deformed real number is based on the geometric idea of invariance by a modular group action. The goal of this lecture is to explain what is a q-rational and a q-irrational, demonstrate beautiful properties of these objects, and describe their relations to many different areas. We also tried to describe some applications of q-numbers.