2016/10/12 by Yuchen Pei, Pei, Yuchen
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CO #math.PR #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1610.03692
Revised version after two rounds of review: added 5 figures; expanded Section 4.2 about qPNG; fixed many typos; clear up the expositions; and more
arxiv created 2017/09/15 · arxiv updated 2017/09/18
In [Matveev-Petrov 2016](arXiv:1504.00666) a q-deformed Robinson-Schensted-Knuth algorithm (qRSK) was introduced. In this article we give reformulations of this algorithm in terms of the Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pairs are swapped in a sense of distribution when the input matrix is transposed. We also formulate a q-polymer model based on the qRSK, prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and q-geometric weights. We use the q-local moves to define a generalisation of the qRSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the q-polymer in q-geometric environment, formulate a q-version of the multilayer polynuclear growth model (qPNG) and write down the joint distribution of the q-polymer partition functions at a fixed time.