The Classical Family Algebra of the Adjoint Representation of sl(n)

2013/06/04 by Matthew Tai, Tai, Matthew
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1306.0867

13 pages

arxiv created 2013/06/04 · openalex publication_date 2013/06/04 · arxiv updated 2013/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the simple Lie algebra g = sl(n,C) we we find a set of generators and relations for the classical family algebra (End(g)⊗ S(g))^G as an algebra over the ring I(g). From these we can then determine a I(g)-linear basis of the family algebra, and thus the generalized exponents of the irreducible components of End(g) viewed as a g-module.

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