The boundary of Young graph with Jack edge multiplicities
| dc.creator | Kerov, Sergei | |
| dc.creator | Okounkov, Andrei | |
| dc.creator | Olshanski, Grigori | |
| dc.date | 1997-03-21 | |
| dc.date.accessioned | 2026-07-07T09:23:55Z | |
| dc.date.available | 2026-07-07T09:23:55Z | |
| dc.description | Consider the lattice of all Young diagrams ordered by inclusion, and denote by Y its Hasse graph. Using the Pieri formula for Jack symmetric polynomials, we endow the edges of the graph Y with formal multiplicities depending on a real parameter $θ$. The multiplicities determine a potential theory on the graph Y. Our main result identifies the corresponding Martin boundary with an infinite-dimensional simplex, the ``geometric boundary'' of the Young graph Y, and provides a canonical integral representation for non-negative harmonic functions. For three particular values of the parameter, the theorem specializes to known results: the Thoma theorem describing characters of the infinite symmetric group, the Kingman's classification of partition structures, and the description of spherical functions of the infinite hyperoctahedral Gelfand pair. | |
| dc.description | 24 pages, 3 pictures (eps), AmS TeX | |
| dc.identifier | https://arxiv.org/abs/q-alg/9703037 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9703037 | |
| dc.identifier | Intern. Math. Research Notices 1998, no. 4, 173-199. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155913 | |
| dc.subject | Quantum Algebra | |
| dc.title | The boundary of Young graph with Jack edge multiplicities | |
| dc.type | text |