On the structure of regular crystals of types A,B,C

Details On the structure of regular crystals of types A,B,C On the structure of regular crystals of types A,B,C

2012-01-22

arxiv.org/abs/1201.4549v2

Mathematics

Combinatorics

52 pages. Compared with the original version, minor corrections and improvements are done

Scientific paper

Regular $A_n$-, $B_n$- and $C_n$-crystals are edge-colored directed graphs, with colors $1,...,n$, related to irreducible highest weight integrable modules over $U_q(\mathfrak{sl}_{n+1})$, $U_q(\mathfrak{sp}_{2n})$ and $U_q(\mathfrak{so}_{2n+1})$, respectively. We present two groups of results on these crystals. First, considering a regular $A_n$-crystal $K$ and using the so-called crossing model from Danilov, Karzanov, and Koshevoy, we characterize all pairwise intersections of maximal connected subcrystals with colors $1,..., n-1$ and colors $2,...,n$ in $K$. This leads to a recursive description of the combinatorial structure of $K$ and provides an efficient algorithm of assembling $K$. Second, we show that any regular $B_n$-crystal (resp. $C_n$-crystal) can be extracted in a certain way from a regular symmetric $A_{2n-1}$-crystal (resp. $A_{2n}$-crystal).

Affiliated with

Also associated with

No associations

Rating

On the structure of regular crystals of types A,B,C 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 crystals of types A,B,C, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the structure of regular crystals of types A,B,C will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-482873