On the structure of regular $B_2$-type crystals
| dc.creator | Danilov, V. I. | |
| dc.creator | Karzanov, A. V. | |
| dc.creator | Koshevoy, G. A. | |
| dc.date | 2006-11-21 | |
| dc.date.accessioned | 2026-07-07T07:33:11Z | |
| dc.date.available | 2026-07-07T07:33:11Z | |
| dc.description | For simply-laced Kac-Moody algebras $\frak g$, Stembridge (2003) proposed a `local' axiomatization of crystal graphs of representations of $U_q(\frak g)$. In this paper we propose axioms for edge-2-colored graphs which characterize the crystals of integrable representations of $U_q(sp(4))$, regular crystal graphs of $B_2$-type. An edge-colored directed graph which obeys our Axioms (K0)--(K5) is called an R-{\em graph} (for brevity), and our main result is that the regular crystals of $B_2$-type are R-graphs and vice versa. We give a direct combinatorial construction for the crystals in question. On this way we introduce a new, so-called {\em crossing model}, which does not exploit Young tableaux. This combinatorial model consists of a two-component graph of a rather simple form and of a certain set of integer-valued functions on its vertices. | |
| dc.description | 29 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/math/0611641 | |
| dc.identifier | http://arxiv.org/abs/math/0611641 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119368 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 17B37, 05C75, 05E99 | |
| dc.title | On the structure of regular $B_2$-type crystals | |
| dc.type | text |