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PBW theorem for affine super Yangian
Abstract
We prove a Poincaré--Birkhoff--Witt theorem for the distinguished affine super Yangian Y=Y1/2,1/2(sl̂(m|n)), where m,n≥2 and m≠ n. With respect to the current filtration, there is a canonical isomorphism grF Y≅ U (uce ( sl(m|n)⊗ℂ[z±1,u] )), where uce denotes the universal central extension. For any totally ordered classical basis homogeneous in parity and current degree, ordered supermonomials in arbitrary fixed filtered lifts form a vector-space basis of Y, with odd exponents restricted to zero or one. The proof identifies the classical presentation through Steinberg Lie superalgebras and establishes injectivity using evaluation homomorphisms, iterated coproducts in degreewise completions, and coefficientwise tensor separation.
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BibTeX
@misc{volkov2026theorem,
title = {{PBW theorem for affine super Yangian}},
author = {Vasiliy Volkov and Vladimir Stukopin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38952},
eprint = {2610.38952},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38952},
}
RIS
TY - UNPB
TI - PBW theorem for affine super Yangian
AU - Vasiliy Volkov
AU - Vladimir Stukopin
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38952
UR - https://arxiv.org/abs/2610.38952
AB - We prove a Poincaré--Birkhoff--Witt theorem for the distinguished affine super Yangian Y=Y_1/2,1/2(sl̂(m|n)), where m,n≥2 and m≠ n. With respect to the current filtration, there is a canonical isomorphism gr_F Y≅ U (uce ( sl(m|n)⊗ℂ[z^±1,u] )), where uce denotes the universal central extension. For any totally ordered classical basis homogeneous in parity and current degree, ordered supermonomials in arbitrary fixed filtered lifts form a vector-space basis of Y, with odd exponents restricted to zero or one. The proof identifies the classical presentation through Steinberg Lie superalgebras and establishes injectivity using evaluation homomorphisms, iterated coproducts in degreewise completions, and coefficientwise tensor separation.
ER -