The crossing model for regular $A_n$-crystals

V. I. Danilov; A. V. Karzanov; G. A. Koshevoy

The crossing model for regular $A_n$-crystals

表示论 2010-11-15 v2

作者: V. I. Danilov , A. V. Karzanov , G. A. Koshevoy

摘要

A regular $A_n$ -crystal is an edge-colored directed graph, with $n$ colors, related to an irreducible highest weight integrable module over $U_q(sl_{n+1})$ . Based on Stembridge's local axioms for regular simply-laced crystals and a structural characterization of regular $A_2$ -crystals in \cite{DKK-07}, we present a new combinatorial construction, the so-called {\em crossing model}, and prove that this model generates precisely the set of regular $A_n$ -crystals. Using the model, we obtain a series of results on the combinatorial structure of such crystals and properties of their subcrystals.

关键词

crystal bases noncrossing partitions combinatorics

引用

@article{arxiv.math/0612360,
  title  = {The crossing model for regular $A_n$-crystals},
  author = {V. I. Danilov and A. V. Karzanov and G. A. Koshevoy},
  journal= {arXiv preprint arXiv:math/0612360},
  year   = {2010}
}

备注

39 pages, LATEX; minor corrections and improvements; this is the final version to appear in J. of Algebra

The crossing model for regular $A_n$-crystals

摘要

关键词

引用

备注

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