68 citations · 207 across the 35 of their papers we have counts for
39 papers
Quantized Howe-type dualities via Koornwinder polynomials and the X=K phenomenon
Thomas Gerber, Bogdan Ion, Cédric Lecouvey +1
We derive the equality between one-dimensional sums associated with tensor products of Kirillov-Reshetikhin column crystals of classical affine types and Lusztig q-analogues of wei…
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…
Towards a Combinatorial Model for -weight Multiplicities of Simple Lie Algebras (Extended Abstract)
Cédric Lecouvey, Cristian Lenart, Adam Schultze
Kostka-Foulkes polynomials are Lusztig's -analogues of weight multiplicities for irreducible representations of semisimple Lie algebras. It has long been known that these polyno…
Relating three combinatorial formulas for type Whittaker functions
Cristian Lenart, James Sidoli
In this work we study the relationship between several combinatorial formulas for type spherical Whittaker functions. These are spherical functions on -adic groups, which ar…
On Combinatorial Models for Affine Crystals
Carly Briggs, Cristian Lenart, Adam Schultze
The tableau model for Kirillov-Reshetikhin (KR) crystals, which are finite dimensional crystals corresponding to certain affine Lie algebras, is commonly used for its ease of cryst…
New structure on the quantum alcove model with applications to representation theory and Schubert calculus
Takafumi Kouno, Cristian Lenart, Satoshi Naito
The quantum alcove model associated to a dominant weight plays an important role in many branches of mathematics, such as combinatorial representation theory, the theory of Macdona…