Affine geometric crystals in unipotent loop groups
Representation Theory
2010-04-14 v1 Combinatorics
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.1004.2233,
title = {Affine geometric crystals in unipotent loop groups},
author = {Thomas Lam and Pavlo Pylyavskyy},
journal= {arXiv preprint arXiv:1004.2233},
year = {2010}
}
Comments
10 pages