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|Title:||On truncated Weyl modules|
|Abstract:||We study structural properties of truncated Weyl modules. A truncated Weyl module WN(λ) is a local Weyl module for g[t]N=g⊗C[t]tNC[t], where g is a finite-dimensional simple Lie algebra. It has been conjectured that, if N is sufficiently small with respect to λ, the truncated Weyl module is isomorphic to a fusion product of certain irreducible modules. Our main result proves this conjecture when λ is a multiple of certain fundamental weights, including all minuscule ones for simply laced g. We also take a further step towards proving the conjecture for all multiples of fundamental weights by proving that the corresponding truncated Weyl module is isomorphic to a natural quotient of a fusion product of Kirillov–Reshetikhin modules. One important part of the proof of the main result shows that any truncated Weyl module is isomorphic to a Chari–Venkatesh module and explicitly describes the corresponding family of partitions. This leads to further results in the case that g=sl2 related to Demazure flags and chains of inclusions of truncated Weyl modules|
|Editor:||Taylor & Francis|
|Appears in Collections:||IMECC - Artigos e Outros Documentos|
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