201. Generalized Young Walls for Classical Lie Algebras
- Author
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Dong-Uy Shin and Jeong-Ah Kim
- Subjects
Monomial ,Pure mathematics ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,01 natural sciences ,Crystal (programming language) ,Lie algebra ,Combinatorial model ,Isomorphism ,0101 mathematics ,Realization (systems) ,Mathematics - Abstract
In this paper, we introduce an new combinatorial model, which we call generalized Young walls for classical Lie algebras, and we give two realizations of the crystal B(∞) over classical Lie algebras using generalized Young walls. Also, we construct natural crystal isomorphisms between generalized Young wall realizations and other realizations, for example, monomial realization, polyhedral realization and tableau realization. Moreover, as applications, we obtain a crystal isomorphism between two different polyhedral realizations of B(∞).
- Published
- 2018
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