Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties

1998/04/07 by Mark Shimozono, Shimozono, Mark · 3 citations
Mathematics · #05E05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/9804039

25 pages, AMS-LaTeX

arxiv created 1998/04/07 · openalex publication_date 1998/04/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Answering a question of Kuniba, Misra, Okado, Takagi, and Uchiyama, it is shown that certain Demazure characters of affine type A, coincide with the graded characters of coordinate rings of closures of conjugacy classes of nilpotent matrices. This entails a translation of the affine type A crystal theory into the language of tableaux following Nakayashiki and Yamada, for the case of tensor products of the classical crystals indexed by rectangular partitions. In particular the explicit action of the zero-th crystal raising operator on the above crystals is given, and its direct connection with the generalized cocyclage on Littlewood-Richardson tableaux is explained.

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