The spindle property of weight systems of representations of small rank algebraic groups and regular unipotent elements
https://doi.org/10.67268/1812-5093-2026-34-1-18-38
EDN: CBBMGE
Abstract
We study irreducible representations of simple algebraic groups over the field $\mathbb{C}$ of~complex numbers. For groups of type $A_2$, $A_3$ and $C_2$ a generalization of the famous Dynkin theorem on the spindle property of the weight system is obtained. This has made it possible to describe the Jordan normal form of unipotent elements in irreducible representations of such groups, i.e., to determine the dimensions of all Jordan blocks of the images of unipotent elements without finding the number of these blocks.
About the Author
A. A. Osinovskaya
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
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Review
For citations:
Osinovskaya A.A. The spindle property of weight systems of representations of small rank algebraic groups and regular unipotent elements. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):18-38. (In Russ.) https://doi.org/10.67268/1812-5093-2026-34-1-18-38. EDN: CBBMGE
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