#### 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.

Done