The Martin Boundary of the YoungFibonacci Lattice
Abstract
We find the Martin boundary for the YoungFibonacci lattice YF. Along with the lattice of Young diagrams, this is the most interesting example of a differential poset. The Martin boundary construction provides an explicit Poissontype integral representation of nonnegative harmonic functions on YF. The latter are in a canonical correspondence with a set of traces on Okada locally semisimple algebra. The set is known to contain all the indecomposable traces. Presumably, all of the traces in the set are indecomposable, though we have no proof of this conjecture. Using a new explicit product formula for Okada characters, we derive precise regularity conditions under which a sequence of characters of finitedimensional Okada algebras converges to a character of the infinitedimensional one.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.math/9712266
 arXiv:
 arXiv:math/9712266
 Bibcode:
 1997math.....12266G
 Keywords:

 Mathematics  Combinatorics;
 05A16 05E05 31C35
 EPrint:
 30 pages, AmSTeX, uses EPSF, one EPS figure