## View abstract

### Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Thursday, July 15, 13:30 ~ 14:05 UTC-3

## Restriction of square integrable representations

### Jorge Vargas

#### Famaf-CIEM, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakfd44da85f77860b573567368d03941a3').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyfd44da85f77860b573567368d03941a3 = 'v&#97;rg&#97;s' + '&#64;'; addyfd44da85f77860b573567368d03941a3 = addyfd44da85f77860b573567368d03941a3 + 'f&#97;m&#97;f' + '&#46;' + '&#117;nc' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r'; var addy_textfd44da85f77860b573567368d03941a3 = 'v&#97;rg&#97;s' + '&#64;' + 'f&#97;m&#97;f' + '&#46;' + '&#117;nc' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r';document.getElementById('cloakfd44da85f77860b573567368d03941a3').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyfd44da85f77860b573567368d03941a3 + '\'>'+addy_textfd44da85f77860b573567368d03941a3+'<\/a>';

Let $G$ be a semisimple Lie group, and $(\pi,V)$ a irreducible square integrable representation for $G$. Thus, a model for $V$ is the $L^2$-kernel of a elliptic operator on a fiber bundle over the symmetric space $G/K$ attached to $G$. Let $H$ be a closed reductive subgroup for $G$. We say $\pi$ is $H$-discretely decomposable ( $H$-admissible) if the sum of the closed $H$-irreducible subspaces in $V$ is dense in $V$, ($H$-admissible if it is $H$-discretely decomposable and the multiplicity of each irreducible factor is finite). We give criteria for being $H$-$\cdots$ in language of spherical functions as well as in the language of differential intertwining operators. On a basic exposition we will present an overview of some aspects of branching problems and results in Orsted-Vargas, Branching problems in reproducing kernel spaces, Duke mathematical journal, Vol. 169, 3478-3537, 2020 and some consequences.