Abstract: The Robinson-Shensted algorithm is a $1-1$ correspondence between the Symmetric group
$S_n$ and the set of pairs of Standard Young tableaux $(T, T')$ of the same shape. In this context, a left cell is
the set of permutations corresponding to the pairs $(T, T')$ with $T$ fixed and $T'$ varying among the SYT
with shape equal to the shape of $T$.
The double cell of $S_n$ is the set of permutations corresponding to pairs of $SYT$ of a fixed shape.
The concept of left and double cells of a Weyl group, $W$, has its origin in the RS algorithm.
Attached to these cells are finite dimensional representations of the Weyl group.
Both the cells and their corresponding representations play a key role in representation theory.
In a first lecture I will survey the relation between cells, primitive ideals, the category of highest weight modules
and the category of bi-modules.
I will describe examples of left cells representations.
In a second lecture, I will talk about cells consisting of Harish-Chandra modules. These cells can be thought of as generalizations of cells for bi-modules in the context of complex groups. Attached to HC cells are also finite dimensional representations of the Weyl group. In the context of classical groups, I will describe the W-structure of HC cells,
and a geometric parametrization of such cells. I will conclude the second talk with a couple of open questions.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: