A q-Analog of the Hook Walk Algorithm for Random Young Tableaux

  • Authors:

  • S. Kerov

  • Affiliations:

  • Steklov Mathematics Institute, St. Petersburg Branch (POMI), Fontanka 27, St. Petersburg, Russia 191011. Supported by a grant from CRM (Université de Montréal), during its Operato ...

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 1993

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Abstract

A probabilistic algorithm, called the q-hook walk, is defined. For a given Young diagram, it produces a new one by adding a random box with probabilities, depending on a positive parameter q. The corresponding Markov chain in the space of infinite Young tableaux is closely related to the knot invariant of Jones, constructed via traces of Hecke algebras. For q = 1, the algorithm is essentially the hook walk of Greene, Nijenhuis, and Wilf. The q-hook formula and a q-deformation of Young graph are also considered.