Tensor Power Asymptotics for Linearly Reductive Groups
Published:Dec 28, 2025 16:08
•1 min read
•ArXiv
Analysis
This paper investigates the growth of irreducible factors in tensor powers of a representation of a linearly reductive group. The core contribution is establishing upper and lower bounds for this growth, which are crucial for understanding the representation theory of these groups. The result provides insights into the structure of tensor products and their behavior as the power increases.
Key Takeaways
- •Provides bounds on the growth of irreducible factors in tensor powers.
- •The bounds are expressed in terms of the dimension of the representation and the dimension of a maximal unipotent subgroup.
- •Contributes to the understanding of representation theory for linearly reductive groups.
Reference
“The paper proves that there exist upper and lower bounds which are constant multiples of n^{-u/2} (dim V)^n, where u is the dimension of any maximal unipotent subgroup of G.”