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Web bases for the Lie superalgebra gl(1|1)
Abstract
Queffelec--Sartori and Tubbenhauer--Vaz--Wedrich give a diagrammatic web category via generators and relations to describe the subcategory of Rep(gl(m|n)) generated by tensor products of exterior powers of the defining representation. We construct the first explicit bases for homomorphism spaces in the web category for gl(1|1), giving an alternative diagrammatic presentation of this web category, and explore connections to the combinatorics of planar networks. Our basis comes equipped with an algorithm to decompose any web into a linear combination of basis webs, giving an effective way to compute in the gl(1|1)-skein theory.
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BibTeX
@misc{enugandla2026bases,
title = {{Web bases for the Lie superalgebra $\mathfrakgl(1|1)$}},
author = {Pranav Enugandla},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07664},
eprint = {2611.07664},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07664},
}
RIS
TY - UNPB
TI - Web bases for the Lie superalgebra gl(1|1)
AU - Pranav Enugandla
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07664
UR - https://arxiv.org/abs/2611.07664
AB - Queffelec--Sartori and Tubbenhauer--Vaz--Wedrich give a diagrammatic web category via generators and relations to describe the subcategory of Rep(gl(m|n)) generated by tensor products of exterior powers of the defining representation. We construct the first explicit bases for homomorphism spaces in the web category for gl(1|1), giving an alternative diagrammatic presentation of this web category, and explore connections to the combinatorics of planar networks. Our basis comes equipped with an algorithm to decompose any web into a linear combination of basis webs, giving an effective way to compute in the gl(1|1)-skein theory.
ER -