Vertex algebraic intertwining operators among generalized Verma modules for ̂𝔰𝔩(2,ℂ)

McRae, Robert; Yang, Jinwei

doi:10.1090/tran/7012

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

Trans. Amer. Math. Soc. 370 (2018), 2351-2390 Request permission

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.

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