• Corpus ID: 119149760

Crystal interpretation of a formula on the branching rule of types $B_{n}$, $C_{n}$, and $D_{n}$.

@article{Hiroshima2016CrystalIO,
  title={Crystal interpretation of a formula on the branching rule of types \$B\_\{n\}\$, \$C\_\{n\}\$, and \$D\_\{n\}\$.},
  author={Toya Hiroshima},
  journal={arXiv: Quantum Algebra},
  year={2016}
}
  • Toya Hiroshima
  • Published 31 January 2016
  • Physics, Mathematics
  • arXiv: Quantum Algebra
The branching coefficients of the tensor product of finite-dimensional irreducible $U_{q}(\mathfrak{g})$-modules, where $\mathfrak{g}$ is $\mathfrak{so}(2n+1,\mathbb{C})$ ($B_{n}$-type), $\mathfrak{sp}(2n,\mathbb{C})$ ($C_{n}$-type), and $\mathfrak{so}(2n,\mathbb{C})$ ($D_{n}$-type), are expressed in terms of Littlewood-Richardson (LR) coefficients in the stable region. We give an interpretation of this relation by Kashiwara's crystal theory by providing an explicit surjection from the LR… 

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References

SHOWING 1-10 OF 14 REFERENCES
Super Duality and Crystal Bases for Quantum Ortho-Symplectic Superalgebras
Let $\mathcal{O}^{int}_q(m|n)$ be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type $B, C, D$ introduced in the author's previous work. It is a natural
Super duality and crystal bases for quantum ortho-symplectic superalgebras II
Let $$\mathcal {O}^\mathrm{int}_q(m|n)$$Oqint(m|n) be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type B, C, D introduced in Kwon (Int Math Res Not, 2015.
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
Combinatorial extension of stable branching rules for classical groups
We give new combinatorial formulas for decomposition of the tensor product of integrable highest weight modules over the classical Lie algebras of type $B, C, D$, and the branching decomposition of
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
Modification Rules and Products of Irreducible Representations of the Unitary, Orthogonal, and Symplectic Groups
Modification rules, expressible in terms of the removal of continuous boundary hooks, are derived which relate nonstandard irreducible representations (IR's) of the unitary, orthogonal, and
Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras
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
Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras
We shall give a generalization of the Littlewood-Richardson rule forUq(g) associated with, the classical Lie algebras by use of crystal base. This rule describes explicitly the decomposition of
A symplectic jeu de taquin bijection between the tableaux of King and of De Concini
The definitions, methods, and results are entirely combinatorial. The symplectic jeu de taquin algorithm developed here is an extension of Schützenberger’s original jeu de taquin and acts on a skew
Introduction to Quantum Groups and Crystal Bases
Lie algebras and Hopf algebras Kac-Moody algebras Quantum groups Crystal bases Existence and uniqueness of crystal bases Global bases Young tableaux and crystals Crystal graphs for classical Lie
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