##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Robert Laudone

#### University of Wisconsin

## Representation stability for 0-Hecke algebras

##### Abstract:

The category {\bf FI} and its variants have been of great interest recently. Being a finitely generated {\bf FI}-module implies many desirable properties about sequences of symmetric group representations, in particular representation stability. We define a new combinatorial category analogous to {\bf FI} for the 0-Hecke algebra, denoted by $\mathcal{H}$, indexing sequences of representations of $H_n(0)$ as $n$ varies under suitable compatibility conditions. We then provide examples of $\mathcal{H}$-modules and use these to discuss some properties finitely generated $\mathcal{H}$-modules possess, including a new form of representation stability and eventually polynomial growth.

Host: Steven Sam

### May 28, 2019

### 2:00 PM

### AP&M 7321

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