Half Potential on Geometric Crystals and Connectedness of Cellular Crystals
| Autor: | Kanakubo, Yuki, Nakashima, Toshiki |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For any simple complex algebraic group, we define upper/lower half-decorated geometric crystals and show that their tropicalization will be upper/lower normal Kashiwara's crystals. In particular, we show that the tropicalization of the half-decorated geometric crystal on the big Bruhat cell(=$B^-_{w_0}:=B^-\cap U\bar w_0 U$) is isomorphic to the crystal $B(\infty)$ of the nilpotent subalgebra of quantum group $U_q^-(\mathfrak g)$. As an application, we shall show that any cellular crystal associated with a reduced word is connected in the sense of a crystal graph. Comment: The gap in the proof has been filled. Some theorem was added |
| Databáze: | arXiv |
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