68 citations · 207 across the 35 of their papers we have counts for
6 papers · 1 filter
Symmetric and Nonsymmetric Macdonald Polynomials via a Path Model with a Pseudo-crystal Structure
Cristian Lenart, Satoshi Naito, Fumihiko Nomoto +1
In this paper we derive a counterpart of the well-known Ram-Yip formula for symmetric and nonsymmetric Macdonald polynomials of arbitrary type. Our new formula is in terms of a gen…
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…