## 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

- MathematicsSymmetry, 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

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- Mathematics
- 1997

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

- MathematicsNagoya Mathematical Journal
- 2007

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).…

Young tableaux and crystal B(∞) for the exceptional Lie algebra types

- MathematicsJ. Comb. Theory, Ser. A
- 2012

Crystalizing theq-analogue of universal enveloping algebras

- Mathematics
- 1990

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

- Mathematics
- 1998

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

- Mathematics
- 1991

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

- Mathematics
- 2010

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

- Mathematics
- 1970

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…