#### Room 326

#### The Real Robinson-Schensted-Knuth Algorithm

#### Amritanshu Prasad

##### IMSc

*The Robinson-Schensted-Knuth (RSK) correspondence is a bijection from the set of non-negative integer matrices onto the set of pairs of semistandard Young tableaux (SSYT) of the same shape.*

Gelfand-Tsetlin (GT) patterns arise in the study of eigenvalues of top minors of Hermitian matrices. It turns out that SSYT can be expressed as integral GT-patterns.

When the RSK correspondence is written in terms of GT-patterns, it turns out to be the restriction to integer points of a volume-preserving piecewise linear map from the space of non-negative real matrices onto a space of real GT-patterns. We will explain how Viennot's light-and-shadows algorithm for the RSK correspondence can be generalized to compute the PL-version of the correspondence on real numbers.

This talk is based on work in progress, in collaboration with Maria Cueto and Sachin Gautam.

Done