Path generating transforms
| dc.creator | Foda, Omar | |
| dc.creator | Lee, Keith S. M. | |
| dc.creator | Pugai, Yaruslav | |
| dc.creator | Welsh, Trevor A. | |
| dc.date | 1998-10-07 | |
| dc.date.accessioned | 2026-07-07T07:37:21Z | |
| dc.date.available | 2026-07-07T07:37:21Z | |
| dc.description | We study combinatorial aspects of q-weighted, length-L Forrester-Baxter paths, P^{p, p'}_{a, b, c}(L), where p, p', a, b, c \in Z_{+}, 0 < p < p', 0 < a, b, c < p', c = b \pm 1, L+a-b \equiv 0 (mod 2), and p and p' are co-prime. We obtain a bijection between P^{p, p'}_{a, b, c}(L) and partitions with certain prescribed hook differences. Thereby, we obtain a new description of the q-weights of P^{p, p'}_{a, b, c}(L). Using the new weights, and defining s_0 and r_0 to be the smallest non-negative integers for which |p s_0 - p' r_0|=1, we restrict the discussion to P^{p, p'}_{s_0} \equiv P^{p, p'}_{s_0,s_0,s_0+1}(L), and introduce two combinatorial transforms: 1. A Bailey-type transform B: P^{p, p'}_{s_0}(L) -> P^{p, p'+p}_{s_0 + r_0}(L'), L \leq L', 2. A duality-type transform D: P^{p, p'}_{s_0}(L) -> P^{p'-p, p'}_{s_0}(L). We study the action of B and D, as q-polynomial transforms on the P^{p, p'}_{s_0}(L) generating functions, χ^{p, p'}_{s_0}(L). In the limit L -> \infinity, χ^{p, p'}_{s_0}(L) reduces to the Virasoro characters, χ^{p, p'}_{r_0, s_0}, of minimal conformal field theories M^{p, p'}, or equivalently, to the one-point functions of regime-III Forrester-Baxter models. As an application of the B and D transforms, we re-derive the constant-sign expressions for χ^{p, p'}_{r_0, s_0}, first derived by Berkovich and McCoy. | |
| dc.identifier | https://arxiv.org/abs/math/9810043 | |
| dc.identifier | http://arxiv.org/abs/math/9810043 | |
| dc.identifier | q-Series from a contemporary perspective (South Hadley, MA, 1998), 157--186, Contemp. Math. 254, Amer. Math. Soc., Providence, RI, 2000. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120749 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Path generating transforms | |
| dc.type | text |