Yangian action conjecture for the twisted affine module L(Λn){\cal L}(\Lambda_n)

From papers

Let L(Λn){\cal L}(\Lambda_n) be the level 11 integrable module of A2n(2)A^{(2)}_{2n}, and let Y(Bn)Y(B_n) be the Yangian of type BnB_n. Suppose

chL(Λn)(q,x)=κBSqt(κ)sκL(x),\operatorname{ch}{\cal L}(\Lambda_n)(q,x)=\sum_{\kappa\in BS}q^{t(\kappa)}s^{\rm L}_{\kappa}(x),

where BSBS is the set of border strips with final part 2n2n. Yangian action conjecture. There is a canonical action of Y(Bn)Y(B_n) on L(Λn){\cal L}(\Lambda_n), and the displayed decomposition describes its Y(Bn)Y(B_n)-module structure. The conjecture extends the preceding character-level expectation from individual border-strip characters to the entire twisted affine module; no proof is supplied in the paper.

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Sources & referencesView supporting material

Primary source

Anatol N. Kirillov, Atsuo Kuniba and Tomoki Nakanishi, “Skew Young diagram method in spectral decomposition of integrable lattice models”, arXiv:q-alg/9607027 (1996).

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