Compatibility of the Feigin-Frenkel isomorphism and the Harish-Chandra isomorphism for jet algebras

Kamgarpour, Masoud (2016) Compatibility of the Feigin-Frenkel isomorphism and the Harish-Chandra isomorphism for jet algebras. Transactions of the American Mathematical Society, 368 3: 2019-2038. doi:10.1090/S0002-9947-2014-06419-2


Author Kamgarpour, Masoud
Title Compatibility of the Feigin-Frenkel isomorphism and the Harish-Chandra isomorphism for jet algebras
Journal name Transactions of the American Mathematical Society   Check publisher's open access policy
ISSN 0002-9947
1088-6850
Publication date 2016-03
Sub-type Article (original research)
DOI 10.1090/S0002-9947-2014-06419-2
Open Access Status Not Open Access
Volume 368
Issue 3
Start page 2019
End page 2038
Total pages 20
Place of publication Providence, RI, United States
Publisher American Mathematical Society
Collection year 2017
Language eng
Formatted abstract
Let g be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra h and Weyl group W. Let gn denote the Lie algebra of n-jets on g. A theorem of Raıs and Tauvel and Geoffriau identifies the centre of the category of gn-modules with the algebra of functions on the variety of n-jets on the affine space h∗/W. On the other hand, a theorem of Feigin and Frenkel identifies the centre of the category of critical level smooth modules of the corresponding affine Kac-Moody algebra with the algebra of functions on the ind-scheme of opers for the Langlands dual group. We prove that these two isomorphisms are compatible by defining the higher residue of opers with irregular singularities. We also define generalized Verma and Wakimoto modules and relate them by a nontrivial morphism.
Keyword Irregular opers
Jet algebras
Residue
Verma modules
Wakimoto modules
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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