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Assembling crystals of type A | | Vladimir I. Danilov
; Alexander V. Karzanov
; Gleb A. Koshevoy
; | | Date: |
23 Dec 2012 | | Abstract: | Regular $A_n$-crystals are certain edge-colored directed graphs which are
related to representations of the quantized universal enveloping algebra
$U_q(mathfrak{sl}_{n+1})$. For such a crystal $K$ with colors $1,2,...,n$, we
consider its maximal connected subcrystals with colors $1,...,n-1$ and with
colors $2,...,n$ and characterize the interlacing structure for all pairs of
these subcrystals. This is used to give a recursive description of the
combinatorial structure of $K$ and develop an efficient procedure of assembling
$K$. | | Source: | arXiv, 1212.5771 | | Services: | Forum | Review | PDF | Favorites | |
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