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

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

1998-04-07

arxiv.org/abs/math/9804039v1

Mathematics

Quantum Algebra

25 pages, AMS-LaTeX

Scientific paper

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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