Corpus ID: 140219540

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}
}
  • Eoghan McDowell
  • Published 30 April 2019
  • Mathematics
  • arXiv: Representation Theory
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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