Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236

Explore the multiset approach to arithmetic and its application to the Weyl character formula for representations of simple Lie groups and Lie algebras in this 40-minute lecture. Delve into special cases connected to ADE graphs A1 and A2, corresponding to SU(2) and SU(3) representations, which are crucial in modern particle physics and the Standard Model. Review the three-dimensional sphere in quaternion algebra and briefly discuss mathematician Hermann Weyl. Understand how the Weyl character formula relates to polynumbers rather than complex exponentials, emphasizing the importance of avoiding irrationalities in mathematics and physics. Learn about tensor product representations and their connection to elementary particle interactions, illustrated through SU(2) central polynumbers. Discover how the Weyl character formula in this context relates to tensor product multiplicities and can be computed using integral polynumber algebra. Gain insights into topics explored in the Exceptional Structures in Mathematics and Physics via Dynamics on Graphs series, available to Wild Egg Maths channel members and Patreon supporters.

Central polynumber algebra and a (baby) Weyl character formula | Math Founds 236 | N J Wildberger