Corpus ID: 119559593

FI-modules and the cohomology of modular representations of symmetric groups

@article{Nagpal2015FImodulesAT,
  title={FI-modules and the cohomology of modular representations of symmetric groups},
  author={Rohit Nagpal},
  journal={arXiv: Representation Theory},
  year={2015}
}
  • Rohit Nagpal
  • Published 2015
  • Mathematics
  • arXiv: Representation Theory
  • An FI-module $V$ over a commutative ring $\bf{k}$ encodes a sequence $(V_n)_{n \geq 0}$ of representations of the symmetric groups $(\mathfrak{S}_n)_{n \geq 0}$ over $\bf{k}$. In this paper, we show that for a "finitely generated" FI-module $V$ over a field of characteristic $p$, the cohomology groups $H^t(\mathfrak{S}_n, V_n)$ are eventually periodic in $n$. We describe a recursive way to calculate the period and the periodicity range and show that the period is always a power of $p$. As an… CONTINUE READING