2005/08/05 by Anne Schilling, A. Schilling · 15 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Affine transformation #Algebraic structures and combinatorial models #Crystal (programming language) #Crystal structure #Set (abstract data type) #Type (biology) #math.CO #math.QA #msc:05A19 #msc:17B37 #msc:81R50 #msc:82B23
paper · pdf · doi:10.1155/imrn/2006/97376
published in International Mathematics Research Notices (Oxford University Press) · 20 pages, 1 figure, axodraw and youngtab style file necessary
arxiv created 2005/08/05 · openalex publication_date 2006/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Rigged configurations are combinatorial objects originating from the Bethe ansatz, which label highest-weight crystal elements. In this paper, a new unrestricted set of rigged configurations is introduced for types ADE by constructing a crystal structure on the set of rigged configurations. In type A, an explicit characterization of unrestricted rigged configurations is provided which leads to a new fermionic formula for unrestricted Kostka polynomials or q-supernomial coefficients. The affine crystal structure for type A is obtained as well.