Weight Multiplicities and Young Tableaux Through Affine Crystals

The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Similarly, explicit closed formulas for the multiplicities of maximal weights of affine Kac–Moody algebras are not known in mo...

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Bibliographic Details
Main Authors: Kim, Jang Soo, Lee, Kyu-Hwan, Oh, Se-jin
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2023
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Affine algebraic groups
Combinatorial analysis
Kac-Moody algebras
Quantum groups
Representations of algebras
Young tableaux
ISBN:1470459949, 9781470459949
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary:The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Similarly, explicit closed formulas for the multiplicities of maximal weights of affine Kac–Moody algebras are not known in most cases. In this paper, we study weight multiplicities for both finite and affine cases of classical types for certain infinite families of highest weights modules. We introduce new classes of Young tableaux, called the
Bibliography:March 2023, volume 283, number 1401 (fourth of 7 numbers)
Other authors: Kyu-Hwan Lee, Se-jin Oh
Includes bibliographical references (p. 87-88)
ISBN:1470459949
9781470459949
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1401