21 citations · 267 across the 50 of their papers we have counts for
50 papers
Special Kirillov-Reshetikhin crystals
Il-Seung Jang, Travis Scrimshaw
We give a uniform realization of Kirillov-Reshetikhin crystals , in terms of PBW crystals, for all affine types, , and nodes in the orbit of the node in…
Square root crystals and the square root of
Eric Marberg, Travis Scrimshaw
We introduce a general monoidal category of -root crystals and then study the special case of square root -crystals. The latter objects include Yu's cr…
Denominators of R-matrices, higher Dorey's rules and a generalization of T-systems for quantum affine algebras
Se-jin Oh, Travis Scrimshaw
We construct a higher level analogue of Dorey's rule, which describe certain surjective morphisms between Kirillov--Reshetikhin (KR) modules over quantum affine algebras. Building…
Crystals for shifted key polynomials
Eric Marberg, Travis Scrimshaw
This article continues our study of - and -key polynomials, which are (non-symmetric) "partial" Schur - and -functions as well as "shifted" versions of key polynomials.…
Key and Lascoux polynomials for symmetric orbit closures
Eric Marberg, Travis Scrimshaw
We introduce shifted analogues of key polynomials related to symplectic and orthogonal orbit closures in the complete flag variety. Our definitions are given by applying isobaric d…
On the structure and representation theory of -deformed Clifford algebras
Willie Aboumrad, Travis Scrimshaw
We provide a generalized definition for the quantized Clifford algebra introduced by Hayashi using another parameter that we call the twist. For a field of characteristic not e…
Limit shapes for skew Howe duality
Dan Betea, Anton Nazarov, Travis Scrimshaw
We study large random partitions boxed into a rectangle and coming from skew Howe duality, or alternatively from dual Schur measures. As the sides of the rectangle go to infinity,…
Cellular subalgebras of the partition algebra
Travis Scrimshaw
We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show t…
Free-fermions and canonical Grothendieck polynomials
Shinsuke Iwao, Kohei Motegi, Travis Scrimshaw
We give a presentation of refined (dual) canonical Grothendieck polynomials and their skew versions using free-fermions. Using this, we derive a number of identities, including the…
Crystal invariant theory II: Pseudo-energies
Benjamin Brubaker, Gabriel Frieden, Pavlo Pylyavskyy +1
The geometric crystal operators and geometric -matrices (or geometric Weyl group actions) give commuting actions on the field of rational functions in variables. We study t…
Integrable systems and crystals for edge labeled tableaux
Ajeeth Gunna, Travis Scrimshaw
We introduce the edge Schur functions that are defined as a generating series over edge labeled tableaux. We formulate as the partition function for a solvable lattice…
Crystal invariant theory I: Geometric RSK
Benjamin Brubaker, Gabriel Frieden, Pavlo Pylyavskyy +1
Berenstein and Kazhdan's theory of geometric crystals gives rise to two commuting families of geometric crystal operators acting on the space of complex matrices. Thes…
Skew Howe duality and limit shapes of Young diagrams
Anton Nazarov, Olga Postnova, Travis Scrimshaw
We consider the skew Howe duality for the action of certain dual pairs of Lie groups on the exterior algebra as a pr…
Quasi-solvable lattice models for and Demazure atoms and characters
Valentin Buciumas, Travis Scrimshaw
We construct colored lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters and atoms. We show that our lattice models are not solvabl…
Refined dual Grothendieck polynomials, integrability, and the Schur measure
Kohei Motegi, Travis Scrimshaw
We construct a vertex model whose partition function is a refined dual Grothendieck polynomial, where the states are interpreted as nonintersecting lattice paths. Using this, we sh…
Double Grothendieck polynomials and colored lattice models
Valentin Buciumas, Travis Scrimshaw
We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe d…
Simplicity of tensor products of Kirillov--Reshetikhin modules: nonexceptional affine and G types
Se-jin Oh, Travis Scrimshaw
We show the denominator formulas for the normalized -matrix involving two arbitrary Kirillov--Reshetikhin (KR) modules and in all nonexceptional…
Colored five-vertex models and Lascoux polynomials and atoms
Valentin Buciumas, Travis Scrimshaw, Katherine Weber
We construct an integrable colored five-vertex model whose partition function is a Lascoux atom based on the five-vertex model of Motegi and Sakai [arXiv:1305.3030] and the colored…
Crystal structures for canonical Grothendieck functions
Graham Hawkes, Travis Scrimshaw
We give a -crystal structure on multiset-valued tableaux, hook-valued tableaux, and valued-set tableaux, whose generating functions are the weak symmetric, ca…
K-theoretic crystals for set-valued tableaux of rectangular shapes
Oliver Pechenik, Travis Scrimshaw
In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured th…
Hook-content formula using excited Young diagrams
Anatol N. Kirillov, Travis Scrimshaw
We construct a hook-content formula and its -analog using excited Young diagrams analogous to Naruse's hook-length formula for skew shapes. Furthermore, we show that our hook-co…
Candidate for the crystal for the queer Lie superalgebra
Ben Salisbury, Travis Scrimshaw
It is shown that the direct limit of the semistandard decomposition tableau model for polynomial representations of the queer Lie superalgebra exists, which is believed to be the c…
Existence of Kirillov--Reshetikhin crystals for multiplicity free nodes
Rekha Biswal, Travis Scrimshaw
We show that the Kirillov--Reshetikhin crystal exists when is a node such that the Kirillov--Reshetikhin module has a multiplicity free classical decomposit…
Kirillov-Reshetikhin crystals for type
Rekha Biswal, Travis Scrimshaw
We construct a combinatorial crystal structure on the Kirillov-Reshetikhin crystal in type , where is the unique node in the orbit of in the affine Dyn…