Chari's conjecture for truncated local Weyl modules

Let P+P^+ be the dominant integral weights of cmathfrakslncmathfrak{sl}_n, let cmathcalPclambdacmathcal{P}_{clambda} be the set of decompositions of clambdainP+clambdain P^+ into two dominant weights, and let (clambdacmathrmmax,1,clambdacmathrmmax,2)(clambda^{cmathrm{\max},1},clambda^{cmathrm{\max},2}) be its unique maximal element. For A=cmathbbC[t]/(t2)A=cmathbb C[t]/(t^2), let W0(clambda,2)W_0(clambda,2) denote the local Weyl module at the origin. Chari's truncated-local-Weyl conjecture. For any a1nea2incmathbbCa_1ne a_2incmathbb C,

W0(clambda,2)V(clambdacmathrmmax,1)a1castV(clambdacmathrmmax,2)a2.W_0(clambda,2)\cong V(clambda^{cmathrm{\max},1})_{a_1}cast V(clambda^{cmathrm{\max},2})_{a_2}.

This conjecture identifies the first nontrivial truncated local Weyl module with a two-factor fusion product and is stated as open in the supplied context.

Sources & referencesView supporting material

Primary source

Johannes Flake, Ghislain Fourier and Viktor Levandovskyy, “Gröbner bases for fusion products”, arXiv:2003.05639 (2021).

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