scholarly journals Geometric and unipotent crystals. II. From unipotent bicrystals to crystal bases

2007 ◽  
pp. 13-88 ◽  
Author(s):  
Arkady Berenstein ◽  
David Kazhdan
Keyword(s):  
Crystal Bases

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 for Quantum Superalgebras

2018 ◽  
Author(s):  
Georgia Benkart ◽  
Seok-Jin Kang
Keyword(s):  
Crystal Bases ◽  
Quantum Superalgebras

scholarly journals Existence of Crystal Bases for Kirillov-Reshetikhin Modules of Type $D$

2007 ◽  
Vol 43 (4) ◽  
pp. 977-1004 ◽  
Author(s):  
Masato Okado
Keyword(s):  
Crystal Bases ◽  
Type D

scholarly journals Super duality and crystal bases for quantum ortho-symplectic superalgebras II

2015 ◽  
Vol 43 (3) ◽  
pp. 553-588 ◽  
Author(s):  
Jae-Hoon Kwon
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.

Crystal bases III

1995 ◽  
pp. 237-257
Author(s):  
Jens Jantzen
Keyword(s):  
Crystal Bases

Similarity of crystal bases

1996 ◽  
pp. 177-186 ◽  
Author(s):  
Masaki Kashiwara
Keyword(s):  
Crystal Bases

scholarly journals Generalized Young walls and crystal bases for quantum affine algebra of type $A$

2010 ◽  
Vol 138 (11) ◽  
pp. 3877-3877 ◽  
Author(s):  
Jeong-Ah Kim ◽  
Dong-Uy Shin
Keyword(s):  
Type A ◽  
Quantum Affine Algebra ◽  
Crystal Bases ◽  
Affine Algebra
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