# Journal of the Ramanujan Mathematical Society

Volume 37, Issue 2, June 2022 pp. 109–127.

The representation theory of Sylow 2-subgroups of symmetric groups

**Authors**:
Sridhar Narayanan

**Author institution:**Institute of Mathematical Sciences (HBNI), Taramani, Chennai

**Summary: **
We use binary trees to study the Bratteli diagram of Sylow 2-subgroups of
symmetric groups. We show that it is simple, has a recursive structure, and
self-similarities at all scales. We contrast its subgraph of one-dimensional
representations with the Macdonald tree. We exploit the recursive structure
to find the multiplicities of irreducible characters in the restriction to a
Sylow 2-subgroup of odd-dimensional representations of the symmetric group
S{2}{k}.

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