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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Table of Contents:
  • Introduction -- Affine Kac–Moody algebras -- Crystals and Young walls -- Young tableaux and almost even tableaux -- Lattice paths and triangular arrays -- Dominant maximal weights -- Weight multiplicities and (spin) rigid Young tableaux -- Level <inline-formula content-type="math/mathml"> 2 2 </inline-formula> weight multiplicities: Catalan and Pascal triangles -- Level <inline-formula content-type="math/mathml"> 3 3 </inline-formula> weight multiplicities: Motzkin and Riordan triangles -- Some level <inline-formula content-type="math/mathml"> k k </inline-formula> weight multiplicities when <inline-formula content-type="math/mathml"> k → ∞ k\to \infty </inline-formula>: Bessel triangle -- Standard Young tableaux with a fixed number of rows of odd length