Random Interactions
Quadratic algebras, combinatorial physics and planar automata
by Prof. Xavier Viennot (Univ. of Bordeaux/CNRS, France)
Thursday, February 28, 2013
from
to
(Asia/Kolkata)
at Colaba Campus ( A304 )
at Colaba Campus ( A304 )
Description |
For certain quadratic algebras Q, we introduce the concept of Q-tableaux, which are certain combinatorial objects drawn on the square lattice. These tableaux are equivalent to the notion of a planar automaton. Planar automata is a new concept (not to be confused with cellular automata) which formalizes the idea of recognizing certain "planar figures" drawn on a 2D lattice. Two quadratic algebras well known in physics are good examples of planar automata: the most simple Weyl-Heisenberg algebra defined by the commutation relation UD=DU+Id (creation-annihilation operators in quantum mechanics) and the so-called PASEP algebra defined by the relation DE=ED+E+D, in the physics of dynamical systems far from equilibrium. The associated Q-tableaux are respectively rook placements, permutations and the so-called alternating, tree-like and permutation tableaux. Other examples include non-crossing configurations of paths, tiling, plane partitions and alternating sign matrices. |