#### Room 326

#### Induced representations of dihedral groups from their subgroups and to symmetric groups

#### Amrutha P

##### IISER Thiruvananthapuram

*Given any finite group G, a combinatorial problem one can consider is to describe the decom-*

position of certain characters of G into its irreducible components. We are mainly interested in the cyclic characters of G, which are the induced representations from the cyclic subgroups of G.

Kraskiewicz and Weyman worked this for the case of the Coxeter groups of different types including the symmetric group S(n) , and hyperoctahedral group B(n). Armin et al. gave a new approach to the case of S(n) and gave a short proof of Kraskiewicz and Weyman theorem. The cyclic characters also have a nice connection to a work by Stembridge on the eigenvalues of the representation of groups. In this talk we will answer the induction problem for all the subgroups of the dihedral group, D(n) using the character formula for the induced representations. Further, D(n) can be considered as a subgroup of S(n) and in the later part we will also see the decomposition of representations induced from D(n) to S(n). This is joint work with T. Geetha and T. Bakkyaraj.

Done