# 2003, English, Article edition: Geometric crystal and tropical R for Formula Kuniba, A.; Okado, M.; Takagi, T.; ...

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Bookmark: http://trove.nla.gov.au/version/208336
Physical Description
• text/​html
Published
• Oxford University Press
• 2003-01-01 00:00:00.0
Language
• English

### Edition details

Title
• Geometric crystal and tropical R for Formula
Author
• Kuniba, A.
• Takagi, T.
Published
• Oxford University Press
• 2003-01-01 00:00:00.0
Physical Description
• text/​html
Subjects
Notes
• We construct a geometric crystal for the affine Lie algebra $${D}_{n}^{\left(1\right)}$$ in the sense of Berenstein and Kazhdan. Based on a matrix realization including a spectral parameter, we prove uniqueness and explicit form of the tropical R , the birational map that intertwines products of the geometric crystals. The tropical R commutes with geometric Kashiwara operators and satisfies the Yang-Baxter equation. It is subtraction-free and yields a piecewise linear formula of the combinatorial R for crystals upon ultradiscretization.
• Copyright (C) 2003, Oxford University Press
Language
• English
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