Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type An-1(1), Cn-1(1), A2n-2(2), Dn(2)

In this paper, we consider polyhedral realizations for crystal bases B ( λ ) of irreducible integrable highest weight modules of a quantized enveloping algebra U q ( g ) , where g is a classical affine Lie algebra of type A n - 1 ( 1 ) , C n - 1 ( 1 ) , A 2 n - 2 ( 2 ) or D n ( 2 ) . We will give ex...

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Bibliographic Details
Published in:Letters in mathematical physics 2023-06, Vol.113 (3)
Main Author: Kanakubo, Yuki
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:In this paper, we consider polyhedral realizations for crystal bases B ( λ ) of irreducible integrable highest weight modules of a quantized enveloping algebra U q ( g ) , where g is a classical affine Lie algebra of type A n - 1 ( 1 ) , C n - 1 ( 1 ) , A 2 n - 2 ( 2 ) or D n ( 2 ) . We will give explicit forms of polyhedral realizations in terms of extended Young diagrams or Young walls that appear in the representation theory of quantized enveloping algebras of classical affine type. As an application, a combinatorial description of ε k ∗ functions on B ( ∞ ) will be given.
ISSN:1573-0530
DOI:10.1007/s11005-023-01680-0