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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Hlavní autoři: Kim, Jang Soo, Lee, Kyu-Hwan, Oh, Se-jin
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2023
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Affine algebraic groups
Combinatorial analysis
Kac-Moody algebras
Quantum groups
Representations of algebras
Young tableaux
ISBN:1470459949, 9781470459949
ISSN:0065-9266, 1947-6221
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Shrnutí: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
Bibliografie: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