Twisted Demazure modules, fusion product decomposition and twisted \(Q\)-systems
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Publication:2792396
DOI10.1090/ERT/478zbMATH Open1397.17029arXiv1409.1201OpenAlexW1878826567MaRDI QIDQ2792396
Author name not available (Why is that?)
Publication date: 9 March 2016
Published in: (Search for Journal in Brave)
Abstract: In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the twisted current algebras. These modules are indexed by an -tuple of partitions satisfying a natural compatibility condition. We give three equivalent presentations of these modules and show that for a particular choice of these modules become isomorphic to Demazure modules in various levels for the twisted affine algebras. As a consequence we see that the defining relations of twisted Demazure modules can be greatly simplified. Furthermore, we investigate the notion of fusion products for twisted modules, first defined in cite{FL99} for untwisted modules, and use the simplified presentation to prove a fusion product decomposition of twisted Demazure modules. As a consequence we prove that twisted Demazure modules can be obtained by taking the associated graded modules of (untwisted) Demazure modules for simply-laced affine algebras. Furthermore we give a semi-infinite fusion product construction for the irreducible representations of twisted affine algebras. Finally, we prove that the twisted -sytem defined in cite{HKOTT02} extends to a non-canonical short exact sequence of fusion products of twisted Demazure modules.
Full work available at URL: https://arxiv.org/abs/1409.1201
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