Fractal behavior of tensor powers of the two dimensional space in prime characteristic
Kevin Coulembier, Pavel Etingof, Victor Ostrik, Daniel Tubbenhauer
TL;DR
This paper investigates the fractal-like behavior of the sequence counting indecomposable summands in tensor powers of SL2's vector representation over fields of prime characteristic.
Contribution
It reveals the fractal nature of the sequence and its generating function, highlighting novel properties in positive characteristic representation theory.
Findings
Sequence exhibits fractal behavior similar to Mahler functions
Generating function shows self-similarity in prime characteristic
Provides new insights into tensor power decompositions in modular representation theory
Abstract
We study the number of indecomposable summands in tensor powers of the vector representation of SL2. Our main focus is on positive characteristic where this sequence of numbers and its generating function show fractal behavior akin to Mahler functions.
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