PreprintCC BY 4.0arXiv
Quasideterminants and differential realizations of W-algebras
Abstract
In this work, we study the Hamiltonian reduction, used in constructing finite rectangular W-algebras, of the big-cell differential realization of glnp. We establish an intrinsic factorization of the reduced differential realization, identifying its Yangian action with the coproduct action on a tensor product of n evaluation differential realizations of glp. Corner quasideterminants provide the essential noncommutative mechanism through which Hamiltonian reduction transforms the higher-rank differential realization into a factorized lower-rank Yangian action.
Related
- Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A
- Free-field realizations of 𝒩 = 1 supersymmetric 𝒲-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$
- The Pozhidaev and Cantarini--Kac Constructions of Simple n-Lie Algebras: Distinctions and Realizations
- Rigid dualizing complex for quantum enveloping algebras and algebras of generalized differential operators
- Identities in differential perm algebras
BibTeX
@misc{derkachov2026quasideterminants,
title = {{Quasideterminants and differential realizations of W-algebras}},
author = {Sergey Derkachov and Daniil Getta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31794},
eprint = {2610.31794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31794},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasideterminants and differential realizations of W-algebras
AU - Sergey Derkachov
AU - Daniil Getta
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31794
UR - https://arxiv.org/abs/2610.31794
AB - In this work, we study the Hamiltonian reduction, used in constructing finite rectangular W-algebras, of the big-cell differential realization of gl_np. We establish an intrinsic factorization of the reduced differential realization, identifying its Yangian action with the coproduct action on a tensor product of n evaluation differential realizations of gl_p. Corner quasideterminants provide the essential noncommutative mechanism through which Hamiltonian reduction transforms the higher-rank differential realization into a factorized lower-rank Yangian action.
ER -