2017/11/27 by Fourier, Ghislain, Martins, Victor, Moura, Adriano
#05E10 #06A07 #17B10 #17B70 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1711.09631
We study structural properties of truncated Weyl modules. A truncated Weyl module WN(λ) is a local Weyl module for \mathfrak g[t]N = \mathfrak g ⊗ (\mathbb C[t])/(tN\mathbb C[t]), where \mathfrak 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 \mathfrak 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 \mathfrak g=\mathfraksl2 related to Demazure flags and chains of inclusions of truncated Weyl modules.