#### Hall 123

#### Restriction of representations and metaplectic groups

#### Shiv Prakash Patel

##### IIT Bombay

*Restricting a representation of a group to some of its "nice" subgroups is a way to understand the representation, especially to those subgroups which give multiplicity one or finite multiplicity. I will discuss a few cases of restriction in the study of p-adic groups. One case will be restricting the representations of $GL_2(E)$ to $GL_2(F)$ where $E/F$ is a quadratic extension of $p$-adic fields. In a work of D. Prasad, this restriction is related to another restriction namely, the restriction of representations of $GL_2(E)$ to $D_F^{\times}$, where $D_F$ is the quaternion division algebra over $F$ and $D_F^{\times} \hookrightarrow GL_2(E)$. Prasad relates these two restrictions by a "dichotomy" involving the Jacquet-Langlands correspondence. In another case, we will discuss how a similar restrictions can be studied in the case of the metaplectic cover of GL_2(E), which is not a linear group. *

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