Vertex algebraic intertwining operators among generalized Verma modules for $\widehat {\mathfrak {sl}(2,\mathbb {C})}$
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- by Robert McRae and Jinwei Yang PDF
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Abstract:
We construct vertex algebraic intertwining operators among certain generalized Verma modules for $\widehat {\mathfrak {sl}(2,\mathbb {C})}$ and calculate the corresponding fusion rules. Additionally, we show that under some conditions these intertwining operators descend to intertwining operators among one generalized Verma module and two (generally non-standard) irreducible modules. Our construction relies on the irreducibility of the maximal proper submodules of generalized Verma modules appearing in the Garland-Lepowsky resolutions of standard $\widehat {\mathfrak {sl}(2,\mathbb {C})}$-modules. We prove this irreducibility using the composition factor multiplicities of irreducible modules in Verma modules for symmetrizable Kac-Moody Lie algebras of rank $2$, given by Rocha-Caridi and Wallach.References
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Additional Information
- Robert McRae
- Affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing 100084, People’s Republic of China
- Address at time of publication: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- MR Author ID: 899058
- Email: robert.h.mcrae@vanderbilt.edu
- Jinwei Yang
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- Address at time of publication: Department of Mathematics, Yale University, New Haven, Connecticut 06520
- MR Author ID: 970734
- Email: jinwei.yang@yale.edu
- Received by editor(s): December 14, 2015
- Received by editor(s) in revised form: June 23, 2016
- Published electronically: November 30, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 2351-2390
- MSC (2010): Primary 17B67, 17B69
- DOI: https://doi.org/10.1090/tran/7012
- MathSciNet review: 3748571