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arXiv · 0808.2411

Tropical R maps and Affine Geometric Crystals

Masaki Kashiwara·Toshiki Nakashima·Masato Okado
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Abstract

By modifying the method in [KNO], certain affine geometric crystals are realized in affinization of the fundamental representation $W(\varpi_1)_l$ and the tropical R maps for the affine geometric crystals are described explicitly. We also define prehomogeneous geometric crystals and show that for a positive geometric crystal, the connectedness of the corresponding ultra-discretized crystal is the sufficient condition for prehomogeneity of the positive geometric crystal. Moreover, the uniqueness of tropical R maps is discussed.

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Masaki Kashiwara, Toshiki Nakashima, Masato Okado. 2008-08-18. Tropical R maps and Affine Geometric Crystals. https://arxiv.org/abs/0808.2411

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