Abstract:

The RSK algorithm gives a well-known bijection between multisets of
pairs of integers and semistandard bitableaux. In a work with Erez Lapid
we categorified the RSK transform, by applying it on the multisegments
of the Zelevinsky classification for p-adic general linear groups, thus
producing a new construction for irreducible smooth representations.
I would like to discuss how aspects of this procedure are better
understood through the lens of bases in a quantum group and their quiver
Hecke algebra categorification. Time permits, I will show how a curious
connection between the classical tool of Bernstein-Zelevinsky
derivatives for p-adic groups and the Kashiwara crystal for quantum
groups, links the RSK picture with that of cyclotomic Hecke algebra
 representations.