2004/10/31 by Victor Kreiman, V. Kreiman, V. Lakshmibai +8
Mathematics · #17B67 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.CO #math.RT #msc:17B67
paper · pdf · doi:10.48550/arxiv.math/0411017
18 pages
openalex publication_date 2004/10/31 · arxiv created 2005/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an elementary and easily computable basis for the Demazure modules in the basic representation of the affine Lie algebra sl(n)-hat (and the loop group SL(n)-hat). A novel feature is that we define our basis ``bottom-up'' by raising each extremal weight vector, rather than ``top-down'' by lowering the highest weight vector. Our basis arises naturally from the combinatorics of its indexing set, which consists of certain subsets of the integers first specified by the Kyoto school in terms of crystal operators. We give a new way of defining these special sets in terms of a recursive but very simple algorithm, the roof operator, which is analogous to the left-key construction of Lascoux-Schutzenberger. The roof operator is in a sense orthogonal to the crystal operators.