Description of B(∞) through Kashiwara Embedding for E₆ and E₇ Lie Algebra Types

2015/07/09 by Jin Hong, Hong, Jin, Hyeonmi Lee +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1507.02645

openalex publication_date 2015/07/09 · arxiv created 2016/02/23 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the crystal base B(∞) associated with the negative part of the quantum group for finite simple Lie algebras of types E₆ and E₇. We present an explicit description of B(∞) as the image of a Kashiwara embedding that is in natural correspondence with the tableau description of B(∞).

Related

• Descriptions of the crystal B(∞) for G₂
• Crystal Bases and Young Tableaux
• Crystal \Bla in B(∞) for G₂ type Lie Algebra
• Nakajima monomials and crystals for special linear Lie algebras
• A preparation theorem for the kashiwara b(∞) crystal