English

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.

Keywords

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

R2 v1 2026-06-21T15:09:56.674Z