BGG resolution formula for Lc((2n),)L_c((2n),\emptyset)

Let W=B2n=G(2,1,2n)W=B_{2n}=G(2,1,2n) and let the parameter c=1/(2n)c=1/(2n) be constant. Write Δi\Delta_i and Δ2ni\Delta_{2n-i} for the standard-module sums specified in the preceding theorem, and let Lc((2n),)L_c((2n),\emptyset) be the corresponding Cherednik algebra simple module. BGG resolution conjecture. For 0in0\leq i\leq n, the iith term of the minimal BGG resolution of Lc((2n),)L_c((2n),\emptyset) is Δi\Delta_i, and the (2ni)(2n-i)th term is Δ2ni\Delta_{2n-i}.

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Primary source

Stephen Griffeth and Emily Norton, “Character formulas and Bernstein-Gelfand-Gelfand resolutions for Cherednik algebra modules”, arXiv:1511.00748 (2015).

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