14 Citations
Ju n 20 20 UNIFORM DESCRIPTION OF THE RIGGED CONFIGURATION BIJECTION
- Mathematics
- 2021
We give a uniform description of the bijection Φ from rigged configurations to tensor products of Kirillov–Reshetikhin crystals of the form ⊗N i=1 B ri,1 in dual untwisted types: simply-laced types…
Rigged configuration bijection and proof of the X = M conjecture for nonexceptional affine types
- MathematicsJournal of Algebra
- 2018
Rigged configuration descriptions of the crystals B(∞) and B(λ) for special linear Lie algebras
- Mathematics
- 2017
The rigged configuration realization RC(∞) of the crystal B(∞) was originally presented as a certain connected component within a larger crystal. In this work, we make the realization more concrete…
Uniform description of the rigged configuration bijection
- MathematicsSelecta Mathematica
- 2020
We give a uniform description of the bijection $$\Phi $$ Φ from rigged configurations to tensor products of Kirillov–Reshetikhin crystals of the form $$\bigotimes _{i=1}^N B^{r_i,1}$$ ⨂ i = 1 N B r i…
Rigged Configurations for all Symmetrizable Types
- MathematicsElectron. J. Comb.
- 2017
This paper shows that the rigged configuration model proposed does indeed hold for all symmetrizable types, and gives an easy combinatorial condition that gives a Littlewood-Richardson rule using rigged configurations which is valid in all symmetry-based Kac-Moody types.
Connecting Marginally Large Tableaux and Rigged Configurations via Crystals
- Mathematics
- 2015
We show that the bijection from rigged configurations to tensor products of Kirillov-Reshetikhin crystals extends to a crystal isomorphism between the B(∞)$B(\infty )$ models given by rigged…
LINEAR RECURRENCE RELATIONS IN Q-SYSTEMS VIA LATTICE POINTS IN POLYHEDRA
- MathematicsTransformation Groups
- 2018
We prove that the sequence of the characters of the Kirillov–Reshetikhin (KR) modules Wma$$ {W}_m^{(a)} $$, m ∈ ℤm≥0 associated to a node a of the Dynkin diagram of a complex simple Lie algebra g$$…
An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_{2}^{(1)}$
- Mathematics
- 2021
We construct an explicit algorithm of the static-preserving bijection between the rigged configurations and the highest weight paths of the form (B2,1)⊗L in the G (1) 2 adjoint crystals.
Type $${{\varvec{D}}}_{{\varvec{n}}}^\mathbf{(1)}$$Dn(1) rigged configuration bijection
- Mathematics
- 2017
We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov–Reshetikhin crystals of type $$D^{(1)}_n$$Dn(1) in full generality. We prove the…
Existence of Kirillov–Reshetikhin crystals of typeG2(1)andD4(3)
- MathematicsJournal of Algebra
- 2018
References
SHOWING 1-10 OF 54 REFERENCES
Affine crystal structure on rigged configurations of type $D_{n}^{(1)}$
- Mathematics
- 2011
Extending the work in Schilling (Int. Math. Res. Not. 2006:97376, 2006), we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov–Reshetikhin crystal Br,s…
Crystal Structure on Rigged Configurations and the Filling Map
- MathematicsElectron. J. Comb.
- 2015
Under the bijection between rigged configurations and tensor products of Kirillov-Reshetikhin crystals specialized to a single tensor factor, a new tableaux model is obtained for Kirillovo-Reshevikin crystals.
A CRYSTAL TO RIGGED CONFIGURATION BIJECTION FOR NONEXCEPTIONAL AFFINE ALGEBRAS
- Mathematics
- 2002
Author(s): Okado, Masato; Schilling, Anne; Shimozono, Mark | Abstract: Kerov, Kirillov, and Reshetikhin defined a bijection between highest weight vectors in the crystal graph of a tensor power of…
A Uniform Model for Kirillov–Reshetikhin Crystals II. Alcove Model, Path Model, and $P=X$
- Mathematics
- 2016
Author(s): Lenart, Cristian; Naito, Satoshi; Sagaki, Daisuke; Schilling, Anne; Shimozono, Mark | Abstract: We establish the equality of the specialization $P_\lambda(x;q,0)$ of the Macdonald…
Promotion Operator on Rigged Configurations of Type A
- MathematicsElectron. J. Comb.
- 2010
This paper shows in particular that the bijection between tensor products of type A_n^{(1)} crystals and (unrestricted) rigged configurations is an affine crystal isomorphism.
A Uniform Model for Kirillov–Reshetikhin Crystals I: Lifting the Parabolic Quantum Bruhat Graph
- Mathematics
- 2012
© 2014 © The Author(s) 2014. Published by Oxford University Press. All rights reserved. We lift the parabolic quantum Bruhat graph (QBG) into the Bruhat order on the affine Weyl group and into…
Paths, crystals and fermionic formulae
- Mathematics
- 2001
We introduce a fermionic formula associated with any quantum affine algebra U q (X N (r) . Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable lattice models, we…