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Affine Geometric Crystal of type $G^{(1)}_2$

Quantum Algebra 2007-05-23 v1 Representation Theory

Abstract

We shall realize certain affine geometric crystal of type G2(1)G^{(1)}_2 explicitly in the fundamental representation W(ϖ1)W(\varpi_1). Its explicit form is rather complicated but still keeps a positive structure.

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Cite

@article{arxiv.math/0612858,
  title  = {Affine Geometric Crystal of type $G^{(1)}_2$},
  author = {Toshiki Nakashima},
  journal= {arXiv preprint arXiv:math/0612858},
  year   = {2007}
}

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14 pages