21 citations · 267 across the 50 of their papers we have counts for
33 papers · 1 filter
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…
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…
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…
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…
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…
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…
Rigged configurations and the -involution for generalized Kac--Moody algebras
Ben Salisbury, Travis Scrimshaw
We construct a uniform model for highest weight crystals and for generalized Kac--Moody algebras using rigged configurations. We also show an explicit description of th…
Multiline queues with spectral parameters
Erik Aas, Darij Grinberg, Travis Scrimshaw
Using the description of multiline queues as functions on words, we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues. We show tha…
On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models
Cristian Lenart, Travis Scrimshaw
We show that a tensor product of nonexceptional type Kirillov--Reshetikhin (KR) crystals is isomorphic to a direct sum of Demazure crystals; we do this in the mixed level case and…
Crystal structures for symmetric Grothendieck polynomials
Cara Monical, Oliver Pechenik, Travis Scrimshaw
The symmetric Grothendieck polynomials representing Schubert classes in the -theory of Grassmannians are generating functions for semistandard set-valued tableaux. We construct…
Identities from representation theory
Se-jin Oh, Travis Scrimshaw
We give a new Jacobi--Trudi-type formula for characters of finite-dimensional irreducible representations in type using characters of the fundamental representations and non-…
Hall-Littlewood polynomials and a Hecke action on ordered set partitions
Jia Huang, Brendon Rhoades, Travis Scrimshaw
We construct an action of the Hecke algebra on a quotient of the polynomial ring , where . The dimension of our quotient ring is the…
Virtual Crystals and Nakajima Monomials
Ben Salisbury, Travis Scrimshaw
An explicit description of the virtualization map for the (modified) Nakajima monomial model for crystals is given. We give an explicit description of the Lusztig data for modified…
Rigged configuration bijection and proof of the conjecture for nonexceptional affine types
Masato Okado, Anne Schilling, Travis Scrimshaw
We establish a bijection between rigged configurations and highest weight elements of a tensor product of Kirillov-Reshetikhin crystals for all nonexceptional types. A key idea for…
A uniform approach to soliton cellular automata using rigged configurations
Xuan Liu, Travis Scrimshaw
For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a n…
Uniform description of the rigged configuration bijection
Travis Scrimshaw
We give a uniform description of the bijection from rigged configurations to tensor products of Kirillov--Reshetikhin crystals of the form in dua…
Alcove path model for
Arthur Lubovsky, Travis Scrimshaw
We construct a model for using the alcove path model of Lenart and Postnikov. We show that the continuous limit of our model recovers a dual version of the Littelmann p…