Room 217

Spinorial Representations of symmetric groups

Jyotirmoy Ganguly

IISER Pune

Any irreducible representation of $S_n$ can be realized as an
orthogonal representation. An orthogonal representation is called Spinorial
if the representation
can be lifted to the group $\Pin(n)$, which is a  non-trivial double cover
of $O(n)$.
We will find  conditions for partitions $\lambda$ of $n$ such that the
corresponding
irreducible representations $V_{\lambda} of $S_n$ (Specht Modules) are
Spinorial. This is joint work with Steven Spallone.