#### Alladi Ramakrishnan Hall

#### Regular representaions and Whittaker models

#### Shiv Prakash Patel

##### IIT Delhi

*Let $O$ be the ring of integers of a non-archimedian local field $F$. Let*

$G$ be a split reductive group defined over $O$. The uniqueness of Whittaker

models of the representations of $G(F)$ plays an important role in the

theory of automorphic forms. In this talk, we will discuss Whiitaker models

of representations of $G(O)$. On the other hand, the regular representations

of $G(O)$ have been useful in constructing the supercuspidal representations

of $G(F)$. For $G= GL_{n}$ or $SL_{n}$ we prove the uniqueness of the

Whittaker models for the representations of $G(O)$. In addition, we see that

only regular representations admit Whiitaker models. The proofs are based on

the explicit construction of regular representations.

This is a joint work with Pooja Singla.

Done