#### Alladi Ramakrishnan Hall

#### Webinar: Intermediate Algebraic Structure in the Restriction Problem

#### Nate Harman

##### The University of Chicago

*Zoom Meeting ID: 894 0978 8415.*

The restriction problem refers to understanding in a combinatorial sense the decomposition of an irreducible representation of GL_n as a representation of S_n. In this talk I will discuss some of the intermediate algebraic structures that arise when studying this problem which constrain the symmetric group representations that appear and (hopefully) give some insight into the general problem. Things I will mention include: Representation stability, the rook monoid, the group of monomial matrices, and a certain subalgebra of the universal enveloping algebra which seems to have interesting combinatorial properties.

Done