Block-Toeplitz determinants, chess tableaux, and the type $\hat{A_1}$ Geiss-Leclerc-Schroer $\phi$-map
Representation Theory
2007-07-23 v1 Combinatorics
Abstract
We evaluate the Geiss-Leclerc-Schroer -map for shape modules over the preprojective algebra of type in terms of matrix minors arising from the block-Toeplitz representation of the loop group . Conjecturally these minors are among the cluster variables for coordinate rings of unipotent cells within . In so doing we compute the Euler characteristic of any generalized flag variety attached to a shape module by counting standard tableaux of requisite shape and parity; alternatively by counting chess tableaux of requisite shape and content.
Keywords
Cite
@article{arxiv.0707.3046,
title = {Block-Toeplitz determinants, chess tableaux, and the type $\hat{A_1}$ Geiss-Leclerc-Schroer $\phi$-map},
author = {Jeanne Scott},
journal= {arXiv preprint arXiv:0707.3046},
year = {2007}
}