#### Hall 123

#### Gelfand Model for S_n: A Combinatorial Approach

#### Digjoy Paul

##### IMSc, Chennai

*A representation of a group G is called a Gelfand model for G if it is equivalent to the multiplicity-free direct sum of all the irreducible representations of G.*

In this talk we will recall the Irreps of S_n introducing Standard young tableau (attributed to Young) and describe the Involution model (complex vector space generated by the involutions in S_n (matchings in Kn)) in a combinatorial flavour.

We assume no prior knowledge in advance Representation theory or combinatorics.

Done