Affine Geometric Crystal of type D₄⁽³⁾

2009/11/18 by Mana Igarashi, Toshiki Nakashima, Igarashi, Mana +1 · 1 citation
Mathematics · Physics and Astronomy · #17B37 #17B67 #Advanced Algebra and Geometry #Affine transformation #Algebraic structures and combinatorial models #Computer science #Crystal (programming language) #FOS: Mathematics #Geology #Geometry #Mathematics #Nonlinear Waves and Solitons #Programming language #Pure mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Type (biology) #math.QA #math.RT #msc:17B37 #msc:17B67

paper · pdf · doi:10.48550/arxiv.0911.3556

12 pages

arxiv created 2009/11/18 · openalex publication_date 2009/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We shall realize certain affine geometric crystal of type D₄⁽³⁾ associated with the fundamental representation W(π₁) explicitly . By its explicit form, we see that it has a positive structure.

Citations

• Ultra-discretization of the G^(1)₂-Geometric Crystals to the D^(3)₄-Perfect Crystals

Cited by

• A_n⁽¹⁾-Geometric Crystal corresponding to Dynkin index i=2 and its ultra-discretization

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• Affine Geometric Crystal of type G⁽¹⁾₂
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• Ultra-discretization of the D₄³-Geometric Crystals to the G₂¹-Perfect Crystals