PreprintCC BY 4.0arXiv
Total positivity and symmetric spaces
Abstract
We define a notion of total positivity for the symmetric space G/K by taking the Hausdorff closure of the image of Lusztig's totally positive part G>0 in G/K. We introduce double Bruhat cells for the symmetric space and define their totally positive pieces. We prove a cell decomposition of the totally nonnegative symmetric space, give explicit positive parametrizations of all cells, establish closure relations, and show that the transition maps between the two natural families of parametrizations are subtraction-free.
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BibTeX
@misc{bao2026total,
title = {{Total positivity and symmetric spaces}},
author = {Huanchen Bao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.25516},
eprint = {2606.25516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25516},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Total positivity and symmetric spaces
AU - Huanchen Bao
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2606.25516
UR - https://arxiv.org/abs/2606.25516
AB - We define a notion of total positivity for the symmetric space G/K by taking the Hausdorff closure of the image of Lusztig's totally positive part G_>0 in G/K. We introduce double Bruhat cells for the symmetric space and define their totally positive pieces. We prove a cell decomposition of the totally nonnegative symmetric space, give explicit positive parametrizations of all cells, establish closure relations, and show that the transition maps between the two natural families of parametrizations are subtraction-free.
ER -