English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce a family of indecomposable finite-dimensionalgraded modules for the twisted current algebras. These modules are indexed byan $|R^+|$-tuple of partitions $\bxi=(\xi^{\alpha})_{\alpha\in R^+}$ satisfyinga natural compatibility condition. We give three equivalent presentations ofthese modules and show that for a particular choice of $\bxi$ these modulesbecome isomorphic to Demazure modules in various levels for the twisted affinealgebras. As a consequence we see that the defining relations of twistedDemazure modules can be greatly simplified. Furthermore, we investigate thenotion of fusion products for twisted modules, first defined in \cite{FL99} foruntwisted modules, and use the simplified presentation to prove a fusionproduct decomposition of twisted Demazure modules. As a consequence we provethat twisted Demazure modules can be obtained by taking the associated gradedmodules of (untwisted) Demazure modules for simply-laced affine algebras.Furthermore we give a semi-infinite fusion product construction for theirreducible representations of twisted affine algebras. Finally, we prove thatthe twisted $Q$-sytem defined in \cite{HKOTT02} extends to a non-canonicalshort exact sequence of fusion products of twisted Demazure modules.

Twisted Demazure modules, fusion product decomposition and twisted Q--systems