Abstract
We study the PBW-filtration on the highest weight representations V(λ) of the Lie algebras of type A n and C n . This filtration is induced by the standard degree filtration on \(\mathrm {U}(\mathfrak{n}^{-})\). In previous papers, the authors studied the filtration and the associated graded algebras and modules over the complex numbers. The aim of this paper is to present a proof of the results which holds over the integers and hence makes the whole construction available over any field.
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Acknowledgements
The work of Evgeny Feigin was partially supported by the Russian President Grant MK-3312.2012.1, by the Dynasty Foundation, by the AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023, by the RFBR grants 12-01-00070, 12-01-00944, 12-01-33101 and by the Russian Ministry of Education and Science under the grant 2012-1.1-12-000-1011-016.
This study comprises research findings from the ‘Representation Theory in Geometry and in Mathematical Physics’ carried out within The National Research University Higher School of Economics’ Academic Fund Program in 2012, grant No. 12-05-0014. This study was carried out within The National Research University Higher School of Economics’ Academic Fund Program in 2012–2013, research grant No. 11-01-0017.
The work of Ghislain Fourier and Peter Littelmann was partially supported by the priority program ‘Representation Theory’ SPP 1388 of the German Science Foundation.
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Feigin, E., Fourier, G., Littelmann, P. (2013). PBW-filtration over ℤ and Compatible Bases for V ℤ(λ) in Type A n and C n . In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London. https://doi.org/10.1007/978-1-4471-4863-0_3
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DOI: https://doi.org/10.1007/978-1-4471-4863-0_3
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