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A New Young Wall Realization of B(λ)and B(∞)

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Using new combinatorics of Young walls,we give a new construction of the arbitrary level highest weight crystal B(λ)for the quantum affine algebras of types A(22n),D(2)n+1,A(2)2n-1,D(1)n,B(1)n and C(1)n.We show that the crystal consisting of reduced Young walls is isomorphic to the crystal B(λ).Moreover,we provide a new realization of the crystal B(∞o)in terms of reduced virtual Young walls and reduced extended Young walls.

quantum affine algebracrystal basishighest weight crystalYoung wall

Zhaobing Fan、Shaolong Han、Seok-Jin Kang、Young Rock Kim

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Harbin Engineering University,Harbin 150001,China

Korea Research Institute of Arts and Mathematics Asan-si,Chungcheongnam-do,31551,Korea

Graduate School of Education,Hankuk University of Foreign Studies Seoul 02450,Korea

NSF of ChinaNSF of Heilongjiang ProvinceFundamental Research Funds for the Central Universities.S.-J.Kang was supported by the National Foreign Experts ProgramNational Research Foundation of Korea(NRF)was supported by Hankuk University of Foreign Studies Research Fund

12271120JQ2020A001YZ22600106012021R1A2C1011467

2023

10.1142/S100538672300041X

代数集刊(英文版)

代数集刊(英文版)

CSCD北大核心
ISSN：1005-3867
年,卷(期)：2023.30(3)
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