scholarly journals Crystal Bases of q-deformed Kac Modules Over the Quantum Superalgebra Uq(𝔤𝔩(m|n))

2012 ◽  
Vol 2014 (2) ◽  
pp. 512-550 ◽  
Author(s):  
Jae-Hoon Kwon
Keyword(s):  
Crystal Bases ◽  
Kac Modules ◽  
Quantum Superalgebra

scholarly journals Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$

2000 ◽  
Vol 13 (2) ◽  
pp. 295-331 ◽  
Author(s):  
Georgia Benkart ◽  
Seok-Jin Kang ◽  
Masaki Kashiwara
Keyword(s):  
Crystal Bases ◽  
Quantum Superalgebra

Quantum superalgebra osp(2?1)

1991 ◽  
Vol 54 (3) ◽  
pp. 923-930 ◽  
Author(s):  
P. P. Kulish
Keyword(s):  
Quantum Superalgebra

scholarly journals Crystal Bases and Monomials forUq(G2)-Modules

2006 ◽  
Vol 34 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Dong-Uy Shin
Keyword(s):  
Crystal Bases

scholarly journals Crystal Bases and Tensor Product Decompositions of Uq(G2)-Modules

1994 ◽  
Vol 163 (3) ◽  
pp. 675-691 ◽  
Author(s):  
S.J. Kang ◽  
K.C. Misra
Keyword(s):  
Tensor Product ◽  
Crystal Bases

Statement B and Crystal Graphs

2011 ◽  
Author(s):  
Ben Brubaker ◽  
Daniel Bump ◽  
Solomon Friedberg
Keyword(s):  
Weight Vector ◽  
Crystal Bases ◽  
Crystal Graph ◽  
Crystal Graphs ◽  
Definition Of

This chapter translates Statements A and B into Statements A′ and B′ in the language of crystal bases, and explains in this language how Statement B′ implies Statement A′. It first introduces the relevant definition, which is provisional since it assumes that we can give an appropriate definition of boxing and circling for Ω‎. The crystal graph formulation in Statement A′ is somewhat simpler than its Gelfand-Tsetlin counterpart. In particular, in the formulation of Statement A, there were two different Gelfand-Tsetlin patterns that were related by the Schützenberger involution. In the crystal graph formulation, different decompositions of the long element simply result in different paths from the same vertex v to the lowest weight vector.

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