#### IMSc Webinar

#### The Howe duality for the symmetric group

#### Rosa Orellana

##### Dartmouth College

*Seminar link: us02web.zoom.us/j/88380037638?pwd=bjc1UHVtcmp5cnkwSjFCWWFBQVZ3Zz09*

Zoom Meeting ID: 883 8003 7638; Password: Littlewood.

Sminar website: www.imsc.res.in/~amri/algcomb

Classical Howe dualities provide a representation theoretical framework for

classical invariant theory. In the classical Howe duality,

$GL_n(\mathbb{C})$ is dual to $GL_k(\mathbb{C})$ when acting on the

polynomial ring in the variables $x_{i,j}$ where $1\leq i\leq n$ and $1\leq

j\leq k$. In this talk, I will introduce a multiset partition algebra,

$MP_k(n)$, as the Howe dual to the symmetric group $S_n$.

Done