Mathematics – Representation Theory
Scientific paper
2006-11-21
Mathematics
Representation Theory
29 pages, 12 figures
Scientific paper
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.
Danilov Vladimir I.
Karzanov Alexander V.
Koshevoy Gleb A.
No associations
LandOfFree
On the structure of regular $B_2$-type crystals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the structure of regular $B_2$-type crystals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the structure of regular $B_2$-type crystals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-338858