Abstract
We prove stability of the Chari-Pressley-Loktev bases for natural inclusions of local Weyl modules of the current algebra \({\mathfrak {sl}_{2}[t]}\). These modules being known to be Demazure submodules in the level 1 representations of the affine Lie algebra \({\widehat {\mathfrak {sl}_{2}}}\), we obtain, by passage to the direct limit, bases for the level 1 representations themselves.
This is a preview of subscription content, log in via an institution to check access.
Weโre sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Chari, V., Loktev, S.: Weyl, Demazure and fusion modules for the current algebra of \({\mathfrak {sl}}\) r+1. Adv. Math. 207(2), 928โ960 (2006). doi:10.1016/j.aim.2006.01.012
Chari, V., Pressley, A.: Integrable and Weyl modules for quantum affine \(\mathfrak {sl_{2}}\). In: Quantum groups and Lie theory (Durham, 1999), vol. 290 of London Math. Soc. Lecture Note Ser., pp 48โ62. Cambridge Univ. Press, Cambridge (2001)
Chari, V., Pressley, A.: Weyl modules for classical and quantum affine algebras. Represent. Theory 5, 191โ223 (2001). doi:10.1090/S1088-4165-01-00115-7. (electronic)
Fourier, G., Littelmann, P.: Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions. Adv. Math. 211(2), 566โ593 (2007). doi:10.1016/j.aim.2006.09.002
Frenkel, I.B., Kac, V.G.: Basic representations of affine Lie algebras and dual resonance models. Invent. Math. 62(1), 23โ66 (1980). doi:10.1007/BF01391662
Kac, V.G.: Infinite-dimensional Lie algebras, 3rd edn. Cambridge University Press, Cambridge. doi:10.1017/CBO9780511626234 (1990)
Raghavan, K.N., Ravinder, B., Viswanath, S.: Area maximizing Gelfand-Tsetlin patterns, preprint (2014)
Author information
Authors and Affiliations
Corresponding author
Additional information
The second named author acknowledges support from CSIR under the SPM Fellowship scheme. The first and third named authors acknowledge support from DAE under a XII plan project
Rights and permissions
About this article
Cite this article
Raghavan, K.N., Ravinder, B. & Viswanath, S. Stability of the Chari-Pressley-Loktev Bases for Local Weyl Modules of \({\mathfrak {sl}_{2}[t]}\) . Algebr Represent Theor 18, 613โ632 (2015). https://doi.org/10.1007/s10468-014-9508-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10468-014-9508-5