Fractal behavior of tensor powers of the two dimensional space in prime characteristic

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.

arXiv comment41 pages, many figures, revision, to appear in Contemp. Math., comments welcome

References in corpus (9)

• Cellular structures using ${\text{U}}_q$-tilting modules
• Billiards and Tilting Characters for ${\mathrm{SL}}_3$
• The Modular Temperley-Lieb Algebra
• SL2 tilting modules in the mixed case
• Quivers for SL(2) tilting modules
• Growth rates of the number of indecomposable summands in tensor powers
• Monoidal categories, representation gap and cryptography
• Asymptotics in finite monoidal categories
• Perfecting group schemes