Affine geometric crystals in unipotent loop groups

Details Affine geometric crystals in unipotent loop groups Affine geometric crystals in unipotent loop groups

2010-04-13

arxiv.org/abs/1004.2233v1

Mathematics

Representation Theory

10 pages

Scientific paper

We study products of the affine geometric crystal of type A corresponding to symmetric powers of the standard representation. The quotient of this product by the R-matrix action is constructed inside the unipotent loop group. This quotient crystal has a semi-infinite limit, where the crystal structure is described in terms of limit ratios previously appearing in the study of total positivity of loop groups.

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