\texttt{Affine.m} -- \texttt{Mathematica} package for computations in representation theory of finite-dimensional and affine Lie algebras

DOI10.1016/j.cpc.2012.06.014zbMath1301.17001arXiv1107.4681OpenAlexW2070755014MaRDI QIDQ483813

Anton A. Nazarov

Publication date: 17 December 2014

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.4681

zbMATH Keywords

weightsLie algebraroot systemKac-Moody algebraaffine Lie algebrairreducible modules, CFT, integrable systems

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) Software, source code, etc. for problems pertaining to nonassociative rings and algebras (17-04)

Related Items

LieART -- a Mathematica application for Lie algebras and representation theory ⋮ GroupMath: a Mathematica package for group theory calculations ⋮ LieART 2.0 -- a Mathematica application for Lie algebras and representation theory ⋮ Symmetry algebras of stringy cosets ⋮ Chiral primaries in strange metals ⋮ Affine.m

Uses Software

• Mathematica
• LiE
• coxeter
• SF
• Affine
• LambdaTensor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Recursive properties of branching and BGG resolution
• Conformal field theory
• The BRST formulation of \(G/H\) WZNW models
• String functions for affine Lie algebras integrable modules
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Virasoro algebras and coset space models
• Modular and conformal invariance constraints in representation theory of affine algebras
• Machine calculations in Weyl groups
• A Maple package for symmetric functions
• A matrix \(S\) for all simple current extensions
• Folded fans and string functions
• Structure of representations generated by vectors of highest weight
• GENERAL BRANCHING FUNCTIONS OF AFFINE LIE ALGEBRAS
• CHARACTERS FOR COSET CONFORMAL FIELD THEORIES AND MAVERICK EXAMPLES
• Recursive algorithm and branching for nonmaximal embeddings
• Tensor Structures Arising from Affine Lie Algebras. I
• Fast recursion formula for weight multiplicities
• Tensor Structures Arising from Affine Lie Algebras. III
• Introduction to Lie Algebras and Representation Theory