121 citations · 1.4k across the 88 of their papers we have counts for
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Type rigged configuration bijection
Masato Okado, Reiho Sakamoto, Anne Schilling +1
We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov--Reshetikhin crystals of type in full generality. We prove…
A uniform model for Kirillov-Reshetikhin crystals III: Nonsymmetric Macdonald polynomials at and Demazure characters
Cristian Lenart, Satoshi Naito, Daisuke Sagaki +2
We establish the equality of the specialization of the nonsymmetric Macdonald polynomial at with the graded character $\mathop{\rm gch} U_{w}^…
Explicit description of the degree function in terms of quantum Lakshmibai-Seshadri paths
Cristian Lenart, Satoshi Naito, Daisuke Sagaki +2
We give an explicit and computable description, in terms of the parabolic quantum Bruhat graph, of the degree function defined for quantum Lakshmibai-Seshadri paths, or equivalentl…
A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X
Cristian Lenart, Satoshi Naito, Daisuke Sagaki +2
We establish the equality of the specialization of the Macdonald polynomial at with the graded character of a tensor product of "single-column" Kirill…
Quantum Lakshmibai-Seshadri paths and root operators
Cristian Lenart, Satoshi Naito, Daisuke Sagaki +2
We give an explicit description of the image of a quantum LS path, regarded as a rational path, under the action of root operators, and show that the set of quantum LS paths is sta…
A uniform model for Kirillov-Reshetikhin crystals I: Lifting the parabolic quantum Bruhat graph
Cristian Lenart, Satoshi Naito, Daisuke Sagaki +2
We lift the parabolic quantum Bruhat graph into the Bruhat order on the affine Weyl group and into Littelmann's poset on level-zero weights. We establish a quantum analogue of Deod…