# Tensor products of modular representations of $\operatorname{SL}_2(\mathbb{F}_p)$ and a random walk on their indecomposable summands

@article{McDowell2019TensorPO, title={Tensor products of modular representations of \$\operatorname\{SL\}\_2(\mathbb\{F\}\_p)\$ and a random walk on their indecomposable summands}, author={Eoghan McDowell}, journal={arXiv: Representation Theory}, year={2019} }

In this paper we give a novel, concise and elementary proof of the decomposition of tensor products of simple modular $\operatorname{SL}_2(\mathbb{F}_p)$-representations. This result is used to decompose tensor products involving their projective covers and to decompose symmetric squares. We define a Markov chain on the simple modular $\operatorname{SL}_2(\mathbb{F}_p)$-representations via tensoring with a fixed simple module and choosing an indecomposable summand according to a specified… Expand

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