##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Finley McGlade

#### UCSD

## Hecke Modules for $SL_3(\mathbb{Q}_p)$

##### Abstract:

From number theory to knots, Hecke algebras have applications within many areas of mathematics. In this talk we describe a pictorial calculus for computing convolution products in affine Hecke algebras over fields of characteristic zero. Convolution products of this type have been understood since the work of Iwahori and Matsumoto [1965]. However, using results of Parkinson, Ram and Schwer [2006], we can now draw pictures illustrating the rich combinatorial nature of these products. We describe this pictorial calculus in the example of $\mathrm{SL}_3(\mathbb{Q}_p)$. Its applicability is limited to characteristic zero.

### February 10, 2020

### 2:00 PM

### AP&M 7321

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