Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions

Abstract

By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK correspondence. We also investigate birational Weyl group actions related to those algorithms.

63 pages (Revised Version: Introduction is modified. Misprints are also corrected.)

References in corpus (3)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• A study on the fourth q-Painlevé equation
• Birational Weyl group action arising from a nilpotent Poisson algebra

Cited by in corpus (6)

• Geometric Crystal and Tropical R for D^(1)_n
• RSK in last passage percolation: a unified approach
• Affine Weyl group approach to Painlevé equations
• Tropical R and Tau Functions
• A birational lifting of the Stanley-Thomas word on products of two chains
• Interpretations of some parameter dependent generalizations of classical matrix ensembles