17 citations · 102 across the 18 of their papers we have counts for
18 papers
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…
PBW bases and marginally large tableaux in types B and C
Jackson Criswell, Ben Salisbury, Peter Tingley
We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara's infinity crystal in types B and C. The first realization is in terms of marginally larg…
The weight function for monomial crystals of affine type
Luke James, Ben Salisbury
In this work, an expression for the affine weight is calculated for Nakajima monomial crystals in affine types and .
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…
PBW bases and marginally large tableaux in type D
Ben Salisbury, Adam Schultze, Peter Tingley
We give an explicit description of the unique crystal isomorphism between two realizations of in type : that using marginally large tableaux and that using PBW monom…
Combinatorial descriptions of the crystal structure on certain PBW bases
Ben Salisbury, Adam Schultze, Peter Tingley
Using the theory of PBW bases, one can realize the crystal for any semisimple Lie algebra over using Kostant partitions as the underlying set. In fact ther…
Combinatorial descriptions of the crystal structure on certain PBW bases (extended abstract)
Ben Salisbury, Adam Schultze, Peter Tingley
Lusztig's theory of PBW bases gives a way to realize the infinity crystal for any simple complex Lie algebra where the underlying set consists of Kostant partitions. In fact, there…
Rigged configurations and the -involution
Ben Salisbury, Travis Scrimshaw
We give an explicit description of the -involution on the rigged configuration model for .
Rigged configurations for all symmetrizable types
Ben Salisbury, Travis Scrimshaw
In an earlier work, the authors developed a rigged configuration model for the crystal (which also descends to a model for irreducible highest weight crystals via a cut…
Counting Anosov graphs
Meera Mainkar, Matthew Plante, Ben Salisbury
In recent work by Dani and Mainkar, a family of finite simple graphs was used to construct nilmanifolds admitting Anosov diffeomorphisms. Our main object of study is this particula…
Connecting marginally large tableaux and rigged configurations via crystals
Ben Salisbury, Travis Scrimshaw
We show that the bijection from rigged configurations to tensor products of Kirillov-Reshetikhin crystals extends to a crystal isomorphism between the models given by r…
A rigged configuration model for
Ben Salisbury, Travis Scrimshaw
We describe a combinatorial realization of the crystals and using rigged configurations in all symmetrizable Kac-Moody types up to certain conditions. This inclu…
The flush statistic on semistandard Young tableaux
Ben Salisbury
In this note, a statistic on Young tableaux is defined which encodes data needed for the Casselman-Shalika formula.
Young tableaux, canonical bases and the Gindikin-Karpelevich formula
Kyu-Hwan Lee, Ben Salisbury
A combinatorial description of the crystal B(infinity) for finite-dimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establi…
A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1)
Seok-Jin Kang, Kyu-Hwan Lee, Hansol Ryu +1
The classical Gindikin-Karpelevich formula appears in Langlands' calculation of the constant terms of Eisenstein series on reductive groups and in Macdonald's work on p-adic groups…
Combinatorics of the Casselman-Shalika formula in type A
Kyu-Hwan Lee, Philip Lombardo, Ben Salisbury
In the recent works of Brubaker-Bump-Friedberg, Bump-Nakasuji, and others, the product in the Casselman-Shalika formula is written as a sum over a crystal. The coefficient of each…
A combinatorial description of the Gindikin-Karpelevich formula in type A
Kyu-Hwan Lee, Ben Salisbury
A combinatorial description of the crystal for finite-dimensional simple Lie algebras in terms of Young tableaux was developed by J. Hong and H. Lee. Using th…