# Crystal B(λ) as a subset of crystal B(∞) expressed as tableaux for An type

@article{Lee2014CrystalBA,
title={Crystal B($\lambda$) as a subset of crystal B(∞) expressed as tableaux for An type},
author={Hyeonmi Lee},
journal={Journal of Algebra},
year={2014},
volume={400},
pages={142-160}
}
• Hyeonmi Lee
• Published 15 February 2014
• Mathematics
• Journal of Algebra
5 Citations
CRYSTAL B(λ) IN B(∞) FOR G 2 TYPE LIE ALGEBRA
• Mathematics
• 2014
Abstract. A previous work gave a combinatorial description of the crys-tal B(∞), in terms of certain simple Young tableaux referred to as themarginally large tableaux, for ﬁnite dimensional simple
CRYSTAL B() IN B(1) FOR G2 TYPE LIE ALGEBRA
• Mathematics
• 2014
A previous work gave a combinatorial description of the crys- tal B(1), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie
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
Crystal ℬ(λ)$\mathcal {B}(\lambda )$ as a Subset of the Tableau Description of ℬ(∞)$\mathcal {B}(\infty )$ for the Classical Lie Algebra Types
• Mathematics
• 2015
The irreducible highest weight crystal ℬ(λ)$\mathcal {B}(\lambda )$ is known to appear as a connected component within the crystal graph of ℬ(∞)⊗{rλ}$\mathcal {B}(\infty )\otimes \{\mathsf Virtual Crystals and Nakajima Monomials • Mathematics Symmetry, Integrability and Geometry: Methods and Applications • 2018 An explicit description of the virtualization map for the (modified) Nakajima monomial model for crystals is given. We give an explicit description of the Lusztig data for modified Nakajima monomials ## References SHOWING 1-10 OF 17 REFERENCES Crystal Bases and Young Tableaux Let B be the crystal basis of the minus part of the quantized enveloping algebra of a semi-simple Lie algebra. Kashiwara has shown that B has a combinatorial description in terms of an embedding of B Nakajima Monomials and Crystals for Special Linear Lie Algebras Abstract Nakajima introduced a certain set of monomials realizing the irreducible highest weight crystals B(λ). The monomial set can be extended so that it contains crystal B(∞) in addition to B(λ). Crystalizing theq-analogue of universal enveloping algebras For an irreducible representation of theq-analogue of a universal enveloping algebra, one can find a canonical base atq=0, named crystal base (conjectured in a general case and proven forAn, Bn, Cn Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules We give a general way of representing the crystal (base) corresponding to the intgrable highest weight modules of quantum Kac-Moody algebras, which is called polyhedral realizations. This is applied On crystal bases of the$Q\$-analogue of universal enveloping algebras
0. Introduction. The notion of the q-analogue of universal enveloping algebras is introduced independently by V. G. Drinfeld and M. Jimbo in 1985 in their study of exactly solvable models in the
t-Analogs of q-Characters of Quantum Affine Algebras of Type E6, E7, E8
We compute t-analogs of q-characters of all l-fundamental representations of the quantum affine algebras of type $${E}_{6}^{(1)}$$, $${E}_{7}^{(1)}$$, $${E}_{8}^{(1)}$$ by a supercomputer. (Here l-
PERMUTATIONS, MATRICES, AND GENERALIZED YOUNG TABLEAUX
A generalized Young tableau of "shape" (pu p2, — ,Pm), where pi ^ p2 ^ i> pm ^ 1, is an array Y of positive integers yij, for 1 S j ^ Pi, 1 S i ^ m, having monotonically nondecreasing rows and
Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras
• Mathematics
• 1994
The explicit form of the crystal graphs for the finite-dimensional representations of the q-analogue of the universal enveloping algebras of type A, B, C, and D is given in terms of semi-standard