The Robinson-Schensted-Knuth (RSK) correspondence is a bijection between finitely supported countably infinite matrices and pairs of semi-standard Young tableaux with many applications to combinatorics and symmetric functions. Berenstein and Kirillov obtained explicit tropical formulas for the RSK bijection, and also considered geometric lifts of these formulas. Recently, O'Connell and other showed that under the geometric RSK (gRSK) correspondence the Schur functions are replaced by analytic objects called Whittaker functions which are ubiquitous in analytic number theory and physics. They also used gRSK to "lift" the Cauchy-Littlewood identity, which gave an alternative proof of a formula conjectured by Bump and proven by Stade.
We will discuss RSK, its connection to the classical Cauchy-Littlewood identity, and the formulas of Berenstein and Kirillov. We will then explain how to obtain the analog of the Cauchy-Littlewood identity from gRSK. Time permitting, we will also discuss how the classical Cauchy-Littlewood shows up in number theory.
The geometric Robinson-Schensted-Knuth correspondence and Whittaker functions I
Oct. 15, 2013 1pm (MATH 220)
Grad Algebra/Logic
Scott Andrews (CU Boulder) Supercharacter Theories of Unipotent Groups Constructed Via Group Actions, Part 2
The geometric Robinson-Schensted-Knuth correspondence and Whittaker functions I